• Corpus ID: 27299163

Introduction to Ergodic theory

  title={Introduction to Ergodic theory},
  author={M. Mirzakhani},
Hyperbolic dynamics studies the iteration of maps on sets with some type of Lipschitz structure used to measure distance. In a hyperbolic system, some directions are uniformly contracted and others are uniformly expanded. Examples include expanding maps on manifolds, Anosov diffeomorphisms, and the shift map discussed in previous lectures. Hyperbolic dynamical behavior often gives rise to iterated function systems of contracting maps which create complicated fractal limit sets for orbits. An… 
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