Hyperbolicity and Dimension (1071)
Dates: 02-06 December 2013 at CIRM (Marseille, France)
This conference focuses on recent progress in the study of hyperbolic dynamical systems and of fractal dimensions with emphasis on the interplay between them. While on one hand the fractal dimension of a self-similar set can be described in terms of parameters of the iterated function system defining it, the fine structure of a hyperbolic dynamical system can be studied via multifractal analysis, that is, by computing the fractal dimensions of level sets of dynamically meaningful observables.
One of the most important aspects in modern dimension theory of hyperbolic systems is that it unites smooth ergodic theory and fractal geometry. Both fields contribute to and gain from each other. Substantial progress has been made to derive deep stochastic and statistical properties of smooth dynamical systems from dimension-theoretic results. On the other hand, geometric measure theory and especially fractal geometry benefit from modern methods used in hyperbolic dynamics, like new developments in the thermodynamic formalism. Another important issue is the application of dimension theory and hyperbolic systems to long-standing conjectures in number theory, like substantial progress in the Littlewood conjecture or the Duffin-Schaefer conjecture.
List of speakers