Ergodic Theory and Related Topics III: Proceedings of the International Conference held in Güstrow, Germany, October 22–27, 1990

Christoph Bandt, Karsten Keller (auth.), Ulrich Krengel, Karin Richter, Volker Warstat (eds.)9780387554440, 0-387-55444-0, 3540554440

The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.

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Table of contents :
Symbolic dynamics for angle-doubling on the circle I. The topology of locally connected Julia sets….Pages 1-23
Spectral decomposition, periods of cycles and a conjecture of M. Misiurewicz for graph maps….Pages 24-31
The Abramov-Rokhlin formula….Pages 32-35
Expanding attractors with stable foliations of class C 0 ….Pages 36-61
On absolutely focusing mirrors….Pages 62-82
Upper and lower class results for subsequences of the Champernowne number….Pages 83-89
The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps….Pages 90-113
On the construction of generalized measure preserving transformations with given marginals….Pages 114-123
Positive entropy implies infinite L p -multiplicity for p>1….Pages 124-127
On mixing generalized skew products….Pages 128-130
Ergodic properties of the stable foliations….Pages 131-145
Ergodic theorem along a return time sequence….Pages 146-152
Some limit theorems for Markov operators and their applications….Pages 153-162
Generic properties of one-dimensional dynamical systems….Pages 163-173
Hölder continuity of the holonomy maps for hyperbolic basic sets I….Pages 174-191
Peculiar submeasures on finite algebras….Pages 192-197
Invariance principles and central limit theorems for nonadditive, stationary processes….Pages 198-228
Fixed point rays of nonexpansive mappings….Pages 229-233