• Corpus ID: 27299163

Introduction to Ergodic theory

@inproceedings{Mirzakhani2010IntroductionTE,
  title={Introduction to Ergodic theory},
  author={M. Mirzakhani},
  year={2010}
}

• M. Mirzakhani
• Published 2010
• Mathematics

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 important example from Riemannian geometry is given by the geodesic flow on the unit tangent bundle of a closed negatively curved manifold. Many of these systems have the common feature that they can be coded as subshifts of finite type.