Lyapunov exponents for continuous transformations and dimension theory

Luis Barreira; César Silva

doi:10.3934/dcds.2005.13.469

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2005, Volume 13, Issue 2: 469-490. Doi: 10.3934/dcds.2005.13.469

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Lyapunov exponents for continuous transformations and dimension theory

Luis Barreira^1, and
César Silva^2,

1.
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa
2.
Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã

Received: January 2003

Revised: March 2005

Published: February 2005

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Abstract

We generalize the concept of Lyapunov exponent to transformations that are not necessarily differentiable. For fairly large classes of repellers and of hyperbolic sets of differentiable maps, the new exponents are shown to coincide with the classical ones. We also discuss the relation of the new Lyapunov exponents with the dimension theory of dynamical systems for invariant sets of continuous transformations.

Keywords:

Lyapunov exponents,
multiplicative ergodic theorem.

Mathematics Subject Classification: Primary: 34D08, 37C45.

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