This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects.

Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical systems, and the theory of entropy and chaos.

The book is suitable for graduate students and researchers interested in dynamical systems.

Readership

Graduate students and research mathematicians interested in dynamical systems.

Table of Contents

• M. Misiurewicz -- Ergodic natural measures
• T. Downarowicz -- Survey of odometers and Toeplitz flows
• S. Bezuglyi, J. Kwiatkowski, and K. Medynets -- Approximation in ergodic theory, Borel, and Cantor dynamics
• A. H. Dooley -- The critical dimension: An approach to non-singular entropy
• J. Aaronson and M. Lemańczyk -- Exactness of Rokhlin endomorphisms and weak mixing of Poisson boundaries
• M. Barge and J. Kwapisz -- Elements of the theory of unimodular Pisot substitutions with an application to $\beta$-shifts
• W. Huang, S. Shao, and X. Ye -- Mixing via sequence entropy
• V. Baladi -- Anisotropic Sobolev spaces and dynamical transfer operators: $C^\infty$ foliations
• D. Mayer and T. Mühlenbruch -- From the transfer operator for geodesic flows on modular surfaces to the Hecke operators on period functions of $\Gamma_0(n)$
• S. Koch and M. Denker -- Hausdorff dimension for Martin metrics
• M. C. Sullivan -- Twistwise flow equivalence and beyond
• A. Fel'shtyn -- Dynamical zeta functions and symplectic Floer homology
• Y. Vorobets -- Periodic geodesics on generic translation surfaces
• S. Albeverio and A. Kosyak -- Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group
• D. Kleinbock and B. Weiss -- Friendly measures, homogeneous flows and singular vectors
• G. Everest, V. Stangoe, and T. Ward -- Orbit counting with an isometric direction
• M. Schmoll -- Spaces of elliptic differentials
• K. Thomsen -- On the structure of beta shifts
• V. Berthé, S. Ferenczi, and L. Q. Zamboni -- Interactions between dynamics, arithmetics and combinatorics: The good, the bad, and the ugly