Topological Theory of Dynamical Systems

Dear Colleagues,

Since Anosov and Bowen's works, the topological theory of uniformly hyperbolic dynamical systems was rapidly developed, and many fruitful results have been obtained. Topological theory based on non-uniformly hyperbolic dynamical systems is also now developing, and the results obtained in these studies usually play important parts in both the qualitative theory of dynamical systems and the numerical theory of dynamical systems.

This Special Issue will stimulate the study of dynamical systems to explore the new directions and further developments, by collecting recent achievements in the modern topological theory of dynamical systems from the dynamical systems community around the world. Achievements in differentiable settings are also welcome and it is expected that new development in topological theory will be inspired by such research papers.

For this Special Issue, we are particularly seeking contributions on the following three topics:

Topological theory of dynamical systems based on the frameworks of uniformly hyperbolic and non-uniformly hyperbolic dynamical systems (the results in differentiable settings are also welcome).

Topological theory of dynamical systems intertwined with measure theory, ergodic theory, chaos theory, probability theory, combinatorics, and so on.

Survey articles that present significant (new or not so new) open questions on the topological theory of dynamical systems.

Prof. Dr. Kazuhiro Sakai
Dr. Naoya Sumi
Guest Editors

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