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.
Ergodic natural measures by M. Misiurewicz Survey of odometers and Toeplitz flows by T. Downarowicz Approximation in ergodic theory, Borel, and Cantor dynamics by S. Bezuglyi, J. Kwiatkowski, and K. Medynets The critical dimension: An approach to non-singular entropy by A. H. Dooley Exactness of Rokhlin endomorphisms and weak mixing of Poisson boundaries by J. Aaronson and M. Lemanczyk Elements of the theory of unimodular Pisot substitutions with an application to $\beta$-shifts by M. Barge and J. Kwapisz Mixing via sequence entropy by W. Huang, S. Shao, and X. Ye Anisotropic Sobolev spaces and dynamical transfer operators: $C^\infty$ foliations by V. Baladi From the transfer operator for geodesic flows on modular surfaces to the Hecke operators on period functions of $\Gamma 0(n)$ by D. Mayer and T. Muhlenbruch Hausdorff dimension for Martin metrics by S. Koch and M. Denker Twistwise flow equivalence and beyond by M. C. Sullivan Dynamical zeta functions and symplectic Floer homology by A. Fel'shtyn Periodic geodesics on generic translation surfaces by Y. Vorobets Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group by S. Albeverio and A. Kosyak Friendly measures, homogeneous flows and singular vectors by D. Kleinbock and B. Weiss Orbit counting with an isometric direction by G. Everest, V. Stangoe, and T. Ward Spaces of elliptic differentials by M. Schmoll On the structure of beta shifts by K. Thomsen Interactions between dynamics, arithmetics and combinatorics: The good, the bad, and the ugly by V. Berthe, S. Ferenczi, and L. Q. Zamboni.