Graduate level introduction to modern
theoretical physics and mathematics techniques for study of
low-dimensional dynamical systems. The emphasis is on the interplay between
the geometry and the statistical mechanics associated with the
The course has much in common with (and complements)
graduate level field theory and statistical mechanics courses; partition
functions and transfer operators are applied to
computation of correlations and spectra of classical and quantum
The course is aimed at PhD students and
postdoctoral fellows in physics, applied mathematics and mathematics.
A term project
will take the place of a final exam.
The term project will be individually tailored to student's level and research
Historical perspective - chaos, and what to do about it.
Topology of flows - how to enumerate orbits,
Smale horseshoes, entropy.
Dynamics, quantitative - periodic orbits, local stability.
Transfer operators - role of statistical distributions in dynamics.
Thermodynamic formalism - computing measurable averages over chaotic flows.
Spectroscopy of chaotic systems - evolution operators, zeta functions,
Quantum determinants - quantization with the Gutzwiller trace formula.
TEXT will be a baby subset of
Classical and Quantum Chaos: A Cyclist Treatise
lecture notes, available on
http://www.nbi.dk/ChaosBook/ . Weekly homework sets
require both analytic and numerical work.
Tuesday, April 1, 1:30 in Tech L386, with detailed
schedule available on
Lecture topics will be described weekly by e-mail.
Please subscribe to the course
even if you are only interested in a subset of the topics -
send e-mail with text (and no header):