Report on "Weak chaos, infinite ergodic theory, and anomalous dynamics"

Seminar: July 25 - 29 and August 8 - 12, 2011; Workshop: August 1 - 5, 2011

The scientific focus of this three-week conference was on systems exhibiting dynamical randomness in form of weak chaos characterized by zero Lyapunov exponents, where the separation of nearby trajectories is weaker than exponential. Rigorous mathematical results about such systems were recently obtained by infinite ergodic theory, which is an extension of ordinary ergodic theory to dynamical systems with non-normalizable measures. These concepts predict novel nonequilibrium physical properties in form of anomalous dynamics, which can be tested in experiments.

The main purpose of this conference was to initiate cross-disciplinary collaborations between physicists working on both the deterministic and the stochastic aspects of weakly chaotic systems and anomalous dynamics, and mathematicians being active in the relevant branches of dynamical systems and ergodic theory. The workshop week brought together key players in both fields for surveying the state of the art in a quick, compact way. The two seminar weeks served as a forum for in-depth and informal discussions by also comprising a series of advanced lectures to provide review and training for young scientists.

It was a big pleasure to have Prof. Joseph Klafter delivering the Colloquium's talk of the conference on "How strange is strange kinetics". Prof. Klafter, currently president of Tel Aviv University, is one of the pioneers of the stochastic theory of anomalous dynamics. He was joined at this conference by an amazing number of world-class leading scientists working on ergodic theory, dynamical systems theory and the stochastic theory of anomalous dynamics.

Apart from such established experts, we welcomed a large number of highly promising young scientists, ranging from masters students and PhD students to postdocs and young group leaders. Many of these young scientists were already among our invited speakers. All of them had the opportunity to present themselves at the workshop by either giving contributed talks, or by presenting posters during two very lively poster sessions. These sessions were preceded by a special session where all poster presenters advertised their works in form of four minute mini talks. We furthermore awarded prizes for the best three poster presentations, selected by a commision consisting of Profs. Bunimovich, Keller, Sokolov and Vulpiani. During the two weeks of seminar, many young scientists presented contributed talks.

A key to the success of this conference was whether a sound communication between mathematicians and physicists working on quite different aspects in this highly interdisciplinary field of research could be established. As expected, the seminar weeks were much more appreciated in this respect than the workshop. This is exemplified by two special talks given by mathematicians in order to elaborate on specific questions raised in previous talks. Two round table sessions at the end of both workshop weeks were very useful for summarizing interesting open problems. The last one significantly exceeded the allocated period of time because of the lively discussions and contributions by all participants.

Naturally, there was less time for such in-depth discussions during the workshop. However, this week was very useful for making a large international audience of about 90 participants from 17 different countries aware of the most recent, important developments in this new field of research. Feedback from many participants received during and after the conference showed that this combination of in-depth seminars and compact workshop week was very successful for establishing cross-links between these different scientific communities by providing much motivation and inspiration for future research.

We wish to acknowledge the excellent conference organization provided by Katrin Lantsch, which included a very dedicated social programme. Her efforts helped significantly to make this three-week conference a great success.