Dynamical Systems (Lecture Notes in Mathematics) de James C. Alexander

Dynamical Systems: Proceedings of the Special Year Held at the University of Maryland, College Park, 1986-87: Lecture Notes in Mathematics, cartea 1342

James C. Alexander

en Limba Engleză Paperback – 14 sep 1988

The papers in this volume reflect the richness and diversity of the subject of dynamics. Some are lectures given at the three conferences (Ergodic Theory and Topological Dynamics, Symbolic Dynamics and Coding Theory and Smooth Dynamics, Dynamics and Applied Dynamics) held in Maryland between October 1986 and March 1987; some are work which was in progress during the Special Year, and some are work which was done because of questions and problems raised at the conferences. In addition, a paper of John Milnor and William Thurston, versions of which had been available as notes but not yet published, is included.

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Cuprins

Discerning fat Baker’s transformations.- Weakly mixing actions of F? have infinite subgroup actions which are Bernoulli.- Nasu’s simple automorphisms.- Almost Markov and shift equivalent sofic systems.- A note on the existence of periodic solutions of a differential system.- The Barge-Martin decomposition theorem for pointwise nonwandering maps of the interval.- Dynamics of tangent.- Geodesic flow on the two-sphere part II: Ergodicity.- Poincaré sequences in infinite measure spaces and complementing subsets of the integers.- Non-self-similar attractors of hyperbolic iterated function systems.- Enveloping semigroup in ergodic theory and a proof of Moore’s ergodicity theorem.- Ratner’s rigidity theorem for geometrically finite Fuchsian groups.- Counting circles.- Periodic behavior of linear automata.- Basic sets: Sets that determine the dimension of basin boundaries.- Topological conjugacy for 1-block factor maps of subshifts and sofic covers.- Approximately transitive (2) flows and transformations have simple spectrum.- Remarks on recurrence and orbit equivalence of nonsingular endomorphisms.- Ergodic theory of foliations and a theorem of Sacksteder.- Distal flows of non abelian groups with finite codimension.- Automorphisms of suspension flows over the circle.- Sturmian minimal systems associated with the iterates of certain functions on an interval.- Volume growth and topological entropy for random transformations.- Decidability of shift equivalence.- A group rotation factor of a non-rigid Rank-1 map.- Periodic points, decidability and Markov subgroups.- On measures induced on subsystems.- On iterated maps of the interval.- Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts.- Threebernoulli factors that generate an ergodic flow.- Equilibrium states and weighted uniform distribution of closed orbits.- Problems and perspectives in the theory of Markov shifts.- Endomorphisms of the full shift which are bijective on an infinity of periodic subsets.- Spectral multiplicity for non-abelian Morse sequences.- Rectangular Tilings of ?n and free ?n-actions.- Properties of the directional entropy function for cellular automata.- Complexity of functions and entropy.- Nonautonomous linearization.