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Indecomposable Coupled Map Lattices with Non–unique Phase

  • R.S. MacKay
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 671)

Abstract

A compact topologically mixing uniformly hyperbolic attractor for a diffeomorphism of a finite-dimensional manifold with Hölder continuous derivative carries a unique probability measure describing the long-time statistics of the forward orbits of almost all initial conditions in its basin. This was proved [28] by converting the orbits of the dynamical system into symbol sequences from a finite alphabet (indexed by time) and considering them as states of a statistical mechanical spin chain with a certain interaction energy which decays exponentially with separation, so leading to a unique phase. The results have been extended to many classes of non-uniformly hyperbolic system by different approaches (e.g. [30]).

Keywords

Markov Chain Symbolic Dynamic Symbol Sequence Symbolic State Unique Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • R.S. MacKay
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickU.K.

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