![]() Mathematical Sciences Research Institute Publicationsĭynamics, Ergodic Theory, and Geometry Dedicated to Anatole Katok Several sections of this list focus on problems beyond the areas covered in the surveys, and all are sure to inspire and guide further research. The articles are complemented by a fifty-page commented problem list, compiled by the editor with the help of numerous specialists. Among the specific areas of interest are random walks and billiards, diffeomorphisms and flows on surfaces, amenability and tilings. Other articles by Eigen, Feres, Kochergin, Krieger, Navarro, Pinto, Prasad, Rand and Robinson cover subjects in hyperbolic, parabolic and symbolic dynamics as well as ergodic theory. Fisher’s survey on local rigidity of group actions is a broad and up-to-date account of a flourishing subject built on the fact that for actions of noncyclic groups, topological conjugacy commonly implies smooth conjugacy. In symplectic geometry, a fast-growing field having its roots in classical mechanics, Cieliebak, Hofer, Latschev and Schlenk give a definitive survey of quantitative techniques and symplectic capacities, which have become a central research tool. CRC Press, Boca Raton, FL, (1999).In this book, which arose from an MSRI research workshop cosponspored by the Clay Mathematical Institute, leading experts give an overview of several areas of dynamical systems that have recently experienced substantial progress. Stability, symbolic dynamics, and chaos, 2nd ed., Stud. An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, (1995). Ergodic properties of rational mappings with large topological degree, Ann. Principles of Algebraic Geometry, Wiley Classics Library, (1994). Complex dynamics in higher dimension, II, Modern Methods in Complex Analysis, Ann. Laminar currents and birational dynamics, Duke Math. Dynamics of bimeromorphic maps of surfaces, Amer. Product of involutions and fixed points, Alg. New integrable cases of a Cremona transformation: A finite-order orbits analysis, Phys. The discrete Painlevé I equations: Transcendental integrability and asymptotic solutions, J. Energy and invariant measures for birational surface maps, Duke Math. Real and complex dynamics of a family of birational maps of the plane: The golden mean subshift, Amer. ![]() Topological entropy and Arnold complexity for two-dimensional mappings, Phys. Real Arnold complexity versus real topological entropy for birational transformations, J. Real topological entropy versus metric entropy for birational measure-preserving transformations, Phys. Growth complexity spectrum of some discrete dynamical systems, Phys. Topological entropy and complexity for discrete dynamical systems, Phys. Rational dynamical zeta functions for birational transformations, Physica A 264, 264–293, chao-dyn/9807014, (1999).Ībarenkova, N., Anglès d’Auriac, J.-C., Boukraa, S., Hassani, S., and Maillard, J.-M. Publishing, River Edge, NJ, (1999).Ībarenkova, N., Anglès d’Auriac, J.-C., Boukraa, S., Hassani, S., and Maillard, J.-M. From Yang-Baxter equations to dynamical zeta functions for birational transformations, Statistical physics on the eve of the 21st century, 436–490, Ser. Abarenkova, N., Anglès d’Auriac, J.-C., Boukraa, S., Hassani, S., and Maillard, J.-M.
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