On the multifractal formalism of Lyapunov exponents: a survey of recent results

DOI10.1007/978-3-031-41316-2_6OpenAlexW4388000215MaRDI QIDQ6119558

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Publication date: 22 March 2024

Published in: New Trends in Lyapunov Exponents (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-41316-2_6

zbMATH Keywords

variational principleLyapunov exponentsthermodynamic formalismmultifractal formalism

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Fractals (28A80) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Cites Work

• Cocycles with one exponent over partially hyperbolic systems
• Some characterizations of domination
• Lyapunov exponents for products of matrices and multifractal analysis. II: General matrices
• Multifractal analysis for Lyapunov exponents on nonconformal repellers
• The thermodynamic formalism for sub-additive potentials
• Lyapunov spectrum of asymptotically sub-additive potentials
• Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles
• Lyapunov spectrum properties and continuity of the lower joint spectral radius
• Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
• Variational principles and mixed multifractal spectra
• The thermodynamic approach to multifractal analysis
• RECURRENCE, DIMENSION AND ENTROPY
• The joint spectrum
• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• Convex Analysis
• Markov Partitions for Axiom A Diffeomorphisms

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