Lyapunov spectrum for multimodal maps

DOI10.1017/etds.2014.135zbMath1353.37061arXiv1406.4731OpenAlexW3098573122MaRDI QIDQ2828030

Michał Rams, Feliks Przytycki, Katrin Gelfert

Publication date: 24 October 2016

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.4731

zbMATH Keywords

pressureLyapunov exponentsHausdorff dimensiondistortionmultimodal maps

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dimension theory of smooth dynamical systems (37C45)

Related Items (8)

The Lyapunov exponent of holomorphic maps ⋮ Sensitive dependence of geometric Gibbs states at positive temperature ⋮ Geometric pressure in real and complex 1-dimensional dynamics via trees of pre-images and via spanning sets ⋮ HAUSDORFF DIMENSION OF THE IRREGULAR SET IN NON-UNIFORMLY HYPERBOLIC SYSTEMS ⋮ Geometric pressure for multimodal maps of the interval ⋮ Birkhoff spectrum for piecewise monotone interval maps ⋮ Thermodynamic formalism methods in the theory of iteration of mappings in dimension one, real and complex ⋮ Multifractal analysis in non-uniformly hyperbolic interval maps

Cites Work

• Unnamed Item
• Dimension theory for multimodal maps
• Repellers for non-uniformly expanding maps with singular or critical points
• On the Lyapunov spectrum for rational maps
• Natural equilibrium states for multimodal maps
• Large derivatives, backward contraction and invariant densities for interval maps
• New examples of \(S\)-unimodal maps with a sigma-finite absolutely continuous invariant measure
• Non-uniform hyperbolicity in complex dynamics
• The Lyapunov spectrum for conformal expanding maps and Axiom-A surface diffeomorphisms
• Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• The dimension spectrum of some dynamical systems
• A multifractal formalism
• A characterization of hyperbolic potentials of rational maps
• The Lyapunov spectrum is not always concave
• Low-temperature phase transitions in the quadratic family
• On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions
• Multifractal spectra of Birkhoff averages for a piecewise monotone interval map
• The singularity spectrumf(α) for cookie-cutters
• Conical limit set and Poincaré exponent for iterations of rational functions
• Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures. Appendix: On non-renormalizable quadratic polynomials
• Equality of pressures for rational functions
• On the transfer operator for rational functions on the Riemann sphere
• On the completeness of multifractal spectra
• Statistical properties of topological Collet–Eckmann maps
• Thermodynamic formalism for interval maps: inducing schemes
• Hausdorff dimension and conformal measures of Feigenbaum Julia sets

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