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Variational analysis for the multifractal spectra of local entropies and Lyapunov exponents. (English) Zbl 1107.37021

Summary: In a previous article [Chaos Solitons Fractals 13, No. 5, 1037–1042 (2002; Zbl 0998.37005)], the authors have analyzed the multifractal Lyapunov spectrum. Here we continue that study by considering perturbations of the potential and the dynamics to obtain variational expressions for the entropies and Lyapunov spectra. The spirit and the framework of this note is to obtain, beyond hyperbolicity, variational results, some of which are new and some other which have already been derived but under stronger conditions.

MSC:

37C45 Dimension theory of smooth dynamical systems
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37B40 Topological entropy
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Citations:

Zbl 0998.37005
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References:

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