Dynamical systems and ergodic theory Smooth and hyperbolic dynamics Concept
Anosov diffeomorphism
Summary
An Anosov diffeomorphism is a diffeomorphism of a compact manifold for which the whole manifold is a hyperbolic set. At every point it contracts some directions and expands the complementary ones, uniformly. Anosov diffeomorphisms are structurally stable, satisfy Axiom A and admit Markov partitions. The basic examples are the hyperbolic toral automorphisms, such as Arnold's cat map.
Further reading
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| Tag | RCQH8P6DPQ |
|---|---|
| URI | m2://RCQH8P6DPQ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37D20 |
| Specializes | Smooth dynamical system |
| Same as |
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