Predrag Cvitanovic'
Predrag Cvitanovic'
References
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Torus breakdown in the symmetryreduced state space of
the KuramotoSivashinsky system
(with N.B. Budanur),
SIAM J. Appl. Dyn. Syst. (2015), submitted;
arXiv.org:1509.08133
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Relative periodic orbits form the backbone of turbulent pipe flows
(with A.P. Willis and K.Y. Short),
arXiv.org:1504.05825
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Neighborhoods of periodic orbits and the stationary distribution
of a noisy chaotic system
(with J.M. Heninger and D. Lippolis),
Phys. Rev. E (2015), to appear;
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Periodic orbit analysis of a system with continuous symmetry
 A tutorial
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Chaos J. 25, 073112 (2015);
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Periodic eigendecomposition and its application in
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Reduction of the SO(2) symmetry for spatially
extended dynamical systems
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Recurrent flows: The clockwork behind turbulence,
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Cartography of highdimensional flows:
A visual guide to sections and slices
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B. Robbins and E. Siminos),
Chaos 14, 739 (2012);
arXiv.org:1209.4915
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Revealing the state space of turbulent pipe flow by symmetry reduction
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Reduction of continuous symmetries of chaotic flows
by the method of slices
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Continuous symmetry reduction and return maps
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 Geometry of turbulence in wallbounded shear flows:
Periodic orbits,
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Phys. Scr. T 142, 014007 (2010)
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How well can one resolve the state space of a chaotic map?
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Phys. Rev. Lett. 104, 014101 (2010);
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Heteroclinic connections in plane Couette flow
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J. Fluid Mech. 621, 365 (2009); arXiv.org:0808.1865
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Equilibrium and travelingwave solutions of plane Couette flow
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J. Fluid Mech. 638, 243 (2009);
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Unstable recurrent patterns in KuramotoSivashinsky dynamics
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Phys. Rev. E 78, 026208 (2008);
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Stable manifolds and the transition to turbulence in pipe flow
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On state space geometry of the KuramotoSivashinsky flow
in a periodic domain
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SIAM J. Appl. Dyn. Syst. 9, 1 (2010);
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Visualizing the geometry of state space in plane Couette flow
(with J.F. Gibson and J. Halcrow),
J. Fluid Mech. 611, 107 (2008); arXiv.org:0705.3957
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Variational method for locating invariant tori
(with Y. Lan and C. Chandre),
Phys. Rev. E 74, 046206 (2006);
arXiv.org:nlin.CD/0508026
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Wave chaos in elastodynamic cavity scattering
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Europhys. Lett. 72, 534 (2005); arXiv.org:nlin.CD/0108053
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Ground Control to Niels Bohr:
Exploring outer space with atomic physics
(with M.A. Porter);
featured in
I. Peterson, Celestial Atomic Physics,
Science News 168 (Sept. 10, 2005);
Notices Am. Math. Soc. 52, 1020 (2005) 
October 2005 Feature Article;
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Modulated amplitude waves in BoseEinstein condensates
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Phys. Rev. E 69, 047201 (2004);
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Variational method for finding periodic orbits in a general flow
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Phys. Rev. E 69, 016217 (2004);
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 A perturbative analysis of modulated amplitude
waves in BoseEinstein condensates
(with M.A. Porter),
Chaos 14, 739 (2004);
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Diagrammatic Young projection operators for U(n)
(with H. Elvang and A.D. Kennedy),
J. Math. Phys. 46, 043501 (2005);
arXiv.org:hepth/0307186
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Stationary modulatedamplitude waves in
the 1D Complex GinzburgLandau equation
(with Y. Lan and N. Garnier),
Physica D 188, 193 (2004);
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Cycle expansions for intermittent maps
(with R. Artuso, P. Cvitanovi\'c and G. Tanner),
Proc. Theo. Phys. Supp. 150, 1 (2003);
arXiv.org:nlin.CD/0305008
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Periodic orbit theory applied to a chaotically
oscillating gas bubble in water
(with G. Simon, M.T. Levinsen, I. Csabai and Á. Horváth),
Nonlinearity 15, 25 (2002)
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Identification of determinism in noisy neuronal systems
(with M.W. Slutzky and D.J. Mogul),
J. Neuroscience Methods 118, 153 (2002)
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Manipulating epileptiform bursting in the rat
hippocampus using chaos control and adaptive techiques
(with M.W. Slutzky and D.J. Mogul),
IEEE Transactions on Biomedical Engineering 50, 559 (2001)
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Deterministic chaos and noise in three
in vitro hippocampal models of epilepsy
(with M.W. Slutzky and D.J. Mogul),
Annals of Biomedical Engineering 29, 607 (2001)
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Chaotic field theory: A sketch,
Physica A 288, 61 (2000);
arXiv.org:nlin.CD/0001034
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Periodic orbit sum rules for billiards: Accelerating cycle expansions
(with S.F. Nielsen and P. Dahlqvist),
J. Phys. A 32, 6757 (1999); arXiv.org:chaodyn/9901001
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Spectrum of stochastic evolution operators:
Local matrix representation approach
(with C.P. Dettmann, G. Palla, N. Søndergård and G. Vattay),
Phys. Rev. E 60, 3936 (1999); arXiv.org:chaodyn/9904027
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Trace formulas for stochastic evolution operators:
Smooth conjugation method
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Trace formulas for stochastic evolution operators:
Weak noise perturbation theory
(with C.P. Dettmann, R. Mainieri and G. Vattay),
J. Stat. Phys 93, 981 (1998);
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 Bifurcation structures in maps of Hénon type
(with K.T. Hansen), Nonlinearity 11, 1233 (1998)
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 Beyond the periodic orbit theory
(with Kim Hansen, J. Rolf and G. Vattay),
Nonlinearity 11, 1209 (1998);
arXiv.org:chaodyn/9712002
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 Spatiotemporal chaos in terms of unstable recurrent patterns
(with F. Christiansen and V. Putkaradze),
Nonlinearity 10, 55 (1997); arXiv.org:chaodyn/9606016
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 Cycle expansions for intermittent diffusion
(with C.P. Dettmann), Phys. Rev. E 56, 6687 (1997)
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 Cycle expansion for power spectrum
(with A.S. Pikovsky),
Proc. SPIE 2038, 290 (1997)
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Dynamical averaging in terms of periodic orbits,
Physica D 83, 109 (1995)
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 Transport properties of the Lorentz gas in
terms of periodic orbits
(with J.P. Eckmann and P. Gaspard),
Chaos, Solitons & Fractals 6, 113 (1995)
 [45]
 A Fredholm determinant for semiclassical quantization
(with P.E. Rosenqvist, G. Vattay, and H.H. Rugh),
Chaos 3, 619 (1993); arXiv.org:chaodyn/9307014
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 Entire Fredholm determinants for evaluation of
semiclassical and thermodynamical spectra
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Phys. Rev. Lett. 71, 4138 (1993);
arXiv.org:chaodyn/9307012
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 Symmetry decomposition of chaotic dynamics
(with B. Eckhardt), Nonlinearity 6, 277 (1993);
arXiv.org:chaodyn/9303016
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Investigation of the Lorentz Gas in terms of periodic orbits
(with P. Gaspard and T. Schreiber),
Chaos 2, 85 (1992);
arXiv.org:chaodyn/9312003
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Periodic orbit quantization of the anisotropic Kepler problem
(with F. Christiansen), Chaos 2, 61 (1992)
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Periodic orbit theory in classical and quantum mechanics,
Chaos 2, 1 (1992);
reprinted in
M.C. Gutzwiller, The Interplay between Classical
and Quantum Mechanics (AATPT, College Park 2001).
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 Periodic orbit expansions for classical smooth flows
(with B. Eckhardt), J. Phys A 24, L237 (1991)
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 Periodic orbits as the skeleton of
classical and quantum chaos,
Physica D 51, 138 (1991)
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The spectrum of the perioddoubling operator in terms of cycles
(with F. Christiansen and H.H. Rugh),
J. Phys A 23, L713 (1990)
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 Recycling of strange sets: II. Applications
(with R. Artuso and E. Aurell),
Nonlinearity 3, 361 (1990)
 [55]
 Recycling of strange sets: I. Cycle expansions
(with R. Artuso and E. Aurell),
Nonlinearity 3, 325 (1990)
 [56]
 On the modelocking universality for critical circle maps
(with G.H. Gunaratne and M.J. Vinson),
Nonlinearity 3, 873 (1990)
 [57]
 Periodic orbit quantization of chaotic systems
(with B. Eckhardt),
Phys. Rev. Lett. 63, 823 (1989)
 [58]
 Complex universality (with J. Myrheim),
Comm. Math. Phys. 121, 225 (1989)
 [59]
 Phase transitions on strange irrational sets
(with A. Artuso and B. Kenny),
Phys. Rev. A 39, 268 (1989)
 [60]
 Invariant measurement of strange sets in terms of cycles,
Phys. Rev. Lett. 61, 2729 (1988)
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Topological and metric properties of Hénontype attractors
(with G.H. Gunaratne and I. Procaccia),
Phys. Rev. A 38, 1503 (1988)
 [62]
 Fractal aggregates in the complex plane
(with T. Bohr and M.H. Jensen),
Europhys. Lett. 6, 445 (1988)
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 Chaos is good news for physics
(with T. Bohr), Nature 329, 391 (1987)
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 Exploring chaotic motion through periodic orbits
(with D. Auerbach, J.P. Eckmann, G. Gunaratne and I. Procaccia),
Phys. Rev. Lett. 58, 23872389 (1987)
 [65]
 Renormalization, unstable manifolds
and the fractal structure of mode locking
(with M.H. Jensen, L.P. Kadanoff and I. Procaccia),
Phys. Rev. Lett. 55, 343 (1985)
 [66]
 Scaling laws for mode lockings in circle maps
(with B. Shraiman and B. Söderberg),
Phys. Scripta 32, 263 (1985)
 [67]
 Farey organization of the fractional Hall effect,
Phys. Scripta T9, 202 (1985)
 [68]
 Universality in chaos
(or, Feigenbaum for cyclists),
lectures given at
1982 Zakopane School of Theoretical Physics,
Acta Phys. Polonica A65, 203 (1984)
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 Universality for period
ntuplings in complex mappings
(with J. Myrheim),
Phys. Lett. 94A, 329 (1983)
 [70]
 Universalitet i overgang til kaos
(with M.H. Jensen), Fysisk Tidsskrift 80, 82 (1982)
 [71]
 The planar sector of field theories
(with P.G. Lauwers and P.N. Scharbach),
Nucl. Phys. B203, 385 (1982)
 [72]
 Spinors in negative dimensions
(with A.D. Kennedy), Phys. Scripta 26, 5 (1982)
 [73]
 The crossover points in lattice gauge theories
with continuous gauge groups
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Phys. Lett. 105B, 201 (1981)
 [74]
 Negative dimensions and E_{7} symmetry,
Nucl. Phys. B188, 373 (1981)
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 Gauge invariance structure of Quantum Chromodynamics
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Nucl. Phys. B186, 165 (1981)
 [76]
 Planar perturbation expansion,
Phys. Lett. 99B, 49 (1981)
 [77]
 Parton evolution as a branching process
(with P. Hoyer and K. Zalewski),
Nucl. Phys. B176, 429 (1980)
 [78]
 Exact solutions of the AltarelliParisi equations
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 Partons and branching
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Phys. Lett. 85B, 413 (1979)
 [80]
 Color charge algebras in Adler's Chromodynamics
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 [81]
 The number and weights of Feynman diagrams
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Nucl. Phys. B127, 176 (1977)
 [83]
 Quantum Chromodynamics on the massshell,
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Phys. Rev. Lett. 37, 1528 (1976)
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in nonAbelian gauge theories,
Phys. Rev. D14, 1536 (1976)
 [87]
 Midnight rider, Bike World (August 1974)
 [88]
 Sixth order magnetic moment of the electron
(with T. Kinoshita),
Phys. Rev. D10, 4007 (1974)
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New approach to the separation of ultraviolet and infrared
divergences of Feynmanparametric integrals
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FeynmanDyson rules in parametric space (with T. Kinoshita),
Phys. Rev. D10, 3478 (1974)
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 Wideangle behavior of a doublescattering diagram,
Phys. Rev. D10, 338 (1974)
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Sixthorder radiative corrections to the electron magnetic moment
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Phys. Rev. Lett. 29, 1534 (1972)
Books, conference proceedings, and other
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 Chaos: Classical and Quantum
(with R. Artuso, R. Mainieri, G. Tanner, G. Vattay and others),
advanced graduate etextbook ChaosBook.org
(Niels Bohr Institute, 2012; Oxford Univ. Press, to appear)
 [94]
 Geometry of turbulence in wallbounded shear flows:
A stroll through 61,506 dimensions,
(with J.F. Gibson),
an introduction to dynamical theory of turbulence;
ChaosBook.org/tutorials
(Georgia Tech 2012)
 [95]

Knowing when to stop: How noise frees us from determinism
(with D. Lippolis),
in M. Robnik and V.G. Romanovski, eds., Let's Face Chaos
through Nonlinear Dynamics, pp 82126 (Am. Inst. of Phys., Melville,
New York, 2012);
arXiv.org:1206.5506
 [96]

Revealing the state space of turbulent pipe flow by symmetry reduction
(with A.P. Willis and M. Avila),
in Jianxiang Wang, ed.,
Proc. ICTAM 2012 Intern. Congr. Theor. and Appl. Mech.,
(2012)
 [97]

Unstable periodic orbits and
heteroclinic connections in plane Couette flow
(with J. Halcrow, J.F. Gibson and D. Viswanath),
short note for
Gallery of Fluid Motion, APS Division of Fluid Dynamics meeting (2008);
arXiv.org:0810.1974
 [98]
 Geometry of state space in plane Couette flow,
(with J.F. Gibson),
in B. Eckhardt, ed.,
Adv. in Turbulence XII,
Proc. 12th EUROMECH Eur. Turb. Conf., Marburg, 75 (Springer, New York 2009)
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Chaos control of epileptiform bursting in the brain
(with M. W. Slutzky and D. J. Mogul),
in Control of chaos in nonlinear circuits and systems,
by B. W.K. Ling, H. H.C. Iu, and H.K. Lam, eds.,
(World Scientific, Singapore 2009)
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 Group Theory
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birdtracks.eu
(Princeton Univ. Press, Princeton NJ 2008)
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 Field theory,
notes prepared by Ejnar Gyldenkerne
(Nordita, Copenhagen, January 1983);
ChaosBook.org/FieldTheory
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Quantum Field Theory,
lecture notes,
ChaosBook.org/FieldTheory
(Georgia Tech, 2005)
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Tracks, Lie's, and Exceptional Magic,
in B. Julia, P. Moussa and P. Vanhove, eds.,
Number Theory and Physics, Les Houches 2003 Spring School
(Springer, New York 2007)
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Closed complex rays in scattering from elastic voids,
(with A. Wirzba and N. Søndergaard), in B. Nilsson, ed.,
Mathematical Modelling of Wave Phenomena 2005, AIP Conference Proceedings (2006)
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Turbulent fields and their recurrences
(with Y. Lan)
in N. Antoniou, ed.,
Proceed. of
10. Intern. Workshop on Multiparticle Production:
Correlations and Fluctuations in QCD
, pp. 313325
(World Scientific, Singapore 2003);
arXiv.org:nlin.CD/0308006
 [106]

State point forcing permits validation of fixed point locations
during chaotic epileptic bursting in the rat brain
(with D. J. Mogul and M. W. Slutzky),
in IEEE Engineering in Medicine & Biology Soc. Annual Conf.
25, 1921 (2003)
 [107]
 Trace formulas in classical dynamical systems,
in I.V. Lerner, J. Keating and D.E. Khmelnitskii, eds.,
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pp. 85102
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 Quantum fluids and classical determinants
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Classical, Semiclassical and Quantum Dynamics in Atoms
Lecture Notes in Physics 485, 29
(Springer, New York 1997);
arXiv.org:chaodyn/9608012
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 Kvantekaos,
KVANT 5, 1 (1994)
 [110]
 Advection of vector fields by chaotic flows
(with N.J. Balmforth, G.R. Ierley, E.A. Spiegel and G. Vattay),
Stochastic Processes in Astrophysics,
Ann. New York Acad. Sci. 706, 148 (1993);
arXiv.org:chaodyn/9307011
 [111]
 A new determinant for quantum chaos
(with P.E. Rosenqvist),
in G.F. Dell'Antonio, S. Fantoni and V.R. Manfredi, eds.,
From Classical to Quantum Chaos,
Soc. Italiana di Fisica Conf. Proceed. 41,
pp. 5764 (Ed. Compositori, Bologna 1993);
arXiv.org:chaodyn/9304003
 [112]
 Pinball scattering
(with B. Eckhardt, P.E. Rosenqvist, G. Russberg and P. Scherer),
in G. Casati and B. Chirikov, eds., Quantum Chaos
(Cambridge Univ. Press, Cambridge 1994)
 [113]
 Periodic Orbit Theory  theme issue
(edited by P. Cvitanovi\'c),
Chaos 2, 1158 (1992)
 [114]
 Quantum Chaos  Quantum Measurement
(proceedings edited by P. Cvitanovi\'c, with I. Percival
and A. Wirzba) (Kluwer, Dordrecht, 1992)
 [115]
 Kvantes Lykkelige Dag (with Kenneth Krabat),
Naturligvis 20 (1991)
 [116]
 The power of chaos,
in J.H. Kim and J. Stringer, eds.,
Applied Chaos
(John Wiley & Sons, New York 1992)
 [117]
 Chaos, Order and Patterns
(proceedings of a NATO Advanced Institute, Como 1990,
edited by P. Cvitanovi\'c, with R. Artuso and G. Casati)
(Plenum, New York 1991)
 [118]
 Circle maps: irrationally winding,
in C. Itzykson, P. Moussa and M. Waldschmidt, eds.,
Number Theory and Physics,
Les Houches 1989 Spring School
(Springer, New York 1992)
 [119]
 Recycling chaos,
in A. Ferraz, F. Oliveira and R. Osorio, eds.,
Nonlinear Physical Phenomena, Brasilia 1989 Winter School
(World Scientific, Singapore 1990)
 [120]
 Chaos for cyclists, in F. Moss, ed.,
Noise and Chaos in Nonlinear Dynamical Systems
(Cambridge Univ. Press, Cambridge 1990)
 [121]
 Phase transitions on strange sets,
in P. Zweifel, G. Gallavotti and M. Anile, eds.,
Nonlinear Evolution and Chaotic Phenomena,
pp. 349361 (Plenum, New York 1988)
 [122]
 Chaos,
Mathematics and Geometry in Science series,
British Broadcasting Corporation Open University programme
(October 1987)
 [123]
 Chaos and fractals,
Sunday science bookcase show,
Australian National Broadcasting Corporation
(May 1987)
 [124]
 Hausdorff dimension of irrational windings,
in R. Gilmore, ed., Proceedings of the XV International
Colloquium on Group Theoretical Methods in Physics,
pp. 184198 (World Scientific, Singapore, 1987)
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 Renormalization description of transitions
to chaos,
in S. Lundquist, N.H. March and E. Tosatti, eds.,
Order and Chaos in Nonlinear Physical Systems,
pp. 7397 (Plenum, New York 1988)
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 Circle maps in the complex plane
(with M.H. Jensen, L.P. Kadanoff and I. Procaccia),
in L. Pietronero and E. Tosatti, eds.,
Fractals in Physics, Trieste, July 1985
(North Holland, New York, 1985)
 [127]
 Universal scaling laws for maps
on the interval and circle maps,
in R.W. Boyd, L.M. Narducci and M.G. Raymer, eds.,
Instabilities and Dynamics of Lasers and Nonlinear Optical Systems,
(U. of Cambridge Press, Cambridge, 1985)
 [128]
 Universality in Chaos
(Adam Hilger, Bristol, 1984; second expanded edition 1989);
reprint selection edited and with introduction by P. Cvitanovi\'c
 [129]
 Universality in transitions to chaos
(with M.H. Jensen), in
Chaos and universality
(Nordita reprint selection, November 1981)
 [130]

Spin and parity from crossections and angular distributions,
in J. Bjorken et al.,
Notes from the SLAC Theory Workshop on the Psi
(SLACPUB1515, Dec. 7, 1974)
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Divergencefree Feynmanparametric integrals
(Ph.D. Thesis, Cornell Univ., August 1973);
published as the three papers
[90], [89] and [88]
above.
 [132]
 Computer generation of integrands for
Feynman parametric integrals, Cornell preprint CLNS234 (June, 1973) and
Proc. 3rd Coll. on Advanced Comp. Meth. in Theoretical Physics,
(Marseille, 1973)
 [133]
 Measurement of diffusion coefficients
of ribosomes by light mixing spectroscopy,
Physics B.S. Thesis
(Mass. Inst. of Technology, 1969)
In preparation; unpublished preprints
 [134]

Turbulent pipe flow as a guided tour along
the neighborhoods of relative periodic orbits
(with A.P. Willis, M. Farazmand, K.Y. Short and N.B. Budanur),
in preparation, to be submitted to J. Fluid Mech.
 [135]

Turbulent KuramotoSivashinsky system recycled
(with N.B. Budanur and X. Ding),
in preparation
 [136]

Determination of the physical dimension of a dissipative
system by periodic orbits
(with X. Ding, K.A. Takeuchi, E. Siminos, and H. Chaté),
in preparation
 [137]

Perturbation theory in noisy chaos
(with J.M. Heninger and D. Lippolis),
in preparation, to be submitted to Comm. Nonlinear Sci. Numer. Simul.
 [138]

A brief life and death of a torus:
computation of quasiperiodic solutions to
the KuramotoSivashinsky equation
(with A. Fox),
in preparation
 [139]

Slice a heart to keep it ticking: Dreams Of Grand Schemes
(with R.O. Grigoriev),
in preparation
 [140]

Periodic orbits of plane Couette flow
(with J.F. Gibson),
in preparation
 [141]

Continuous symmetry reduced trace formulas,
in preparation
 [142]

Topological partitioning of escape dynamics in planar Crossed Fields problem
(with R. Paskauskas),
in preparation
 [143]

Partially hyperbolic two dimensional invariant tori in
three degree of freedom Hamiltonian systems
(with R. Paskauskas),
in preparation
 [144]

Steady fast kinematic dynamos: the topological entropy bound
and the effect of magnetic field diffusion
(with E. Ott), in preparation
 [145]

Periodic orbit theory of chaotic tunneling
(with O. Sigwarth, S. Creagh and N. Whelan),
in preparation
 [146]

Symbolic dynamics and Markov partitions for the stadium billiard
(with K.T. Hansen), J. Stat. Phys., (accepted 1996,
revised version still not resubmitted);
arXiv.org:chaodyn/9502005
 [147]
 Periodic orbit expansions for power spectra of chaotic systems
(with A.S. Pikovsky and M.J. Feigenbaum),
Rockefeller Univ. preprint (Oct. 1993)
 [148]
 Classical and exceptional Lie algebras
as invariance algebras,
Oxford preprint 40/77 (June, 1977) (unpublished)
 [149]
 More on microcanonical paradigm,
(with M.J. Feigenbaum,
for D. Bensimon, T.C. Halsey, M.H. Jensen,
L.P. Kadanoff, A. Libchaber, I. Procaccia, B.I. Shraiman and
J. Stavans),
(Göteborg 17 Nov. 1985),
rejected from every proceedings submitted to.
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