February  2005, 13(2): 469-490. doi: 10.3934/dcds.2005.13.469

Lyapunov exponents for continuous transformations and dimension theory

1. 

Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

2. 

Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal

Received  January 2003 Revised  March 2005 Published  April 2005

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.
Citation: Luis Barreira, César Silva. Lyapunov exponents for continuous transformations and dimension theory. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 469-490. doi: 10.3934/dcds.2005.13.469
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