## Ergodic Theory and Related Topics III: Proceedings of the International Conference held in Güstrow, Germany, October 22-27, 1990Ulrich Krengel, Karin Richter, Volker Warstat 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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### Contents

Symbolic dynamics for angledoubling on the circle | 1 |

Spectral Decomposition Periods of Cycles and a Conjecture | 2 |

Misiurewicz for Graph Maps | 24 |

Copyright | |

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a-equivalence absolutely focusing angle assume asymptotical stability asymptotically belongs billiards branched manifolds C1 immersion called Cantor set central limit theorem chord compact condition conjugate point consecutive reflections consider constant construction contains continuous function continuous map convergence Corollary covering curvature decomposition defined denote density diffeomorphism disjoint disk dynamical systems endpoints entropy equation equivalent ergodic theory exists expanding attractor finite fixed focusing component following properties geodesic flow gmp-transformation harmonic measure Hausdorff dimension Hausdorff measures Hence homeomorphism implies inequality integrable intersect interval itineraries Julia set lamination Lebesgue Markov operator Math measure preserving transformation Moreover n-disk n-manifold neighbourhood obtain parabolic periodic point positive PQ-interval probability space Proceedings Proof of Theorem proposition prove rational maps real number rectangles Riemannian metric satisfied semigroup sequence slice refinement stochastic sublemma subset subwords tangent topological unique unstable manifolds Xo.N zero