``Chaos" theory can be traced back a century to Poincaré, and to the fundamental contributions of Kolmogorov, Arnold and other great mathematicians, but the modern, physics inspired nonlinear dynamics is a young subject; the current blossoming, which is expected to last for many years to come, has its roots in discoveries of 70's.
``Chaos" research on an international level started relatively early in Denmark. Even before ``chaos" was recognized as a subject, the groups which today form the Center have made important contributions to nonlinear dynamics, such as the 1970 detection of subharmonics in acoustic wave amplification in piezoelectric semiconductors at DTU-FI, the 1974 discovery of multiperiodic oscillations (``burst oscillations") in chemical reactions at HCØ-KI, and the 1977 invention of the unbiased Josephson volt standard at HCØ-FL. Members of the NBI/Nordita group contributed in 1976 to one of the key advances of the modern theory, the period doubling universality at the onset of chaos; in 1981 Nordita published the ``Chaos and Universality" reprint collection, and a year later the first Nordita ``Chaos" summer workshop brought together many of the most distinguished contributors to the field, together with a large number of Nordic participants. In the early 80's, the research in solid state physics and phase transitions at HCØ-FL led to study of the dynamics of mode-locking (phenomena involving competing frequencies), and important contributions were made to this scenario of the onset of chaos at an early stage. A few years later, when the theory of multifractals was developed, members of the NBI/Nordita group again played a central role. Today the Danish nonlinear science is strong and has a high international profile. Besides the groups participating in CATS, there are other strong groups at DTU and Risø National Laboratory, together with smaller but active groups at Å rhus University, Roskilde University Center, and Odense University. The CATS groups collaborate actively with many of these groups, and an important goal for the CATS center is to facilitate and catalyze further cooperation.
The reasons for the existing close CATS collaborations, lie in the complementary profiles of the groups involved. The collaborations formed gradually through the 80's, with some of the present members having worked both at HCØ, DTU and NBI/Nordita, and through jointly organized meetings and workshops. The NBI/Nordita group is the largest one and has established a strong theoretical, condensed matter and mathematical physics research effort, together with the newly started experimental effort. Connections to other theoretical groups (nuclear, high energy, astrophysics, solid state and neural networks) are essential to the group's activity, and the international connections are strong, in keeping with the NBI/Nordita traditions. The main research topics at present are classical and quantum chaos, turbulence and physics of complex systems. The HCØ-KI group has a long tradition for research on nonlinear chemical systems, and has contributed experimentally and theoretically to the understanding of oscillatory chemical reactions. The method of characterizing complex chemical systems developed by the group forms a basis for the joint experimental and theoretical projects on chemical turbulence with the NBI/Nordita groups. The group has also a strong interest in models of biological self-organization and morphogenesis, a CATS theme that it shares with the DTU-FI group. The group at DTU-FI has specialized in applications of nonlinear dynamics to a wide variety of problems ranging from engineering to biology. The group has good connections to industry, and, most importantly, to the medical research. For many years the main interest has been biological applications of nonlinear methods and the group has acquired a unique position in this promising field.
One of the Center's key tasks is to aid the continuity and stability of nonlinear dynamics research at the University of Copenhagen. Until now, a significant part of the research in these new directions has only been possible through temporary support from private foundations. Thus P. Alstrø m, T. Bohr, and P. Cvitanovic are supported by the Novo and Carlsberg foundations, and M.H. Jensen was supported until the end of 1994 by a grant to the University of Copenhagen. Lack of permanent positions has hampered the long term research planning for both students and staff, and the level and quality of the future research activities will depend crucially on the Center's ability to contribute to the renewal of Danish nonlinear physics by providing support for young and dynamic researchers. To secure this goal, the Center provides support for several established scientists on lecturer level, and dedicates part of its funds to postdoctoral and visiting scientist positions.