Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Lyapunov exponents for continuous transformations and dimension theory

Pages: 469 - 490, Volume 13, Issue 2, July 2005      doi:10.3934/dcds.2005.13.469

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Luis Barreira - Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal (email)
César Silva - Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal (email)

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.

Received: January 2003;      Revised: March 2005;      Available Online: April 2005.