Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes

DOI10.1007/s11856-011-0013-9zbMath1218.37042OpenAlexW2039138794MaRDI QIDQ532590

Luis Barreira, Godofredo Iommi

Publication date: 5 May 2011

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/128443

zbMATH Keywords

thermodynamic formalismdimension spectrumentropy spectrumergodic optimization problemparabolic horseshoes

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Related Items

The thermodynamic approach to multifractal analysis ⋮ Multifractal analysis of non-uniformly hyperbolic systems ⋮ Recurrence and transience for suspension flows ⋮ Wild attractors and thermodynamic formalism ⋮ Lyapunov spectrum for Hénon-like maps at the first bifurcation ⋮ Thermodynamic formalism for interval maps: inducing schemes ⋮ Dimension theory for multimodal maps ⋮ Multiple phase transitions on compact symbolic systems ⋮ On the computability of rotation sets and their entropies ⋮ Time change for flows and thermodynamic formalism

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nice inducing schemes and the thermodynamics of rational maps
• Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents
• Ergodic optimization for renewal type shifts
• Equilibrium measures for maps with inducing schemes
• Equilibrium states for interval maps: potentials with \(\sup\varphi- \inf\varphi<h_{\mathrm{top}}(f)\)
• Invariant measures of minimal post-critical sets of logistic maps
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions
• Dimension and product structure of hyperbolic measures
• The zeta function, non-differentiability of pressure, and the critical exponent of transition
• The fish has no bones
• Multifractal analysis of Lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to diophantine approximation
• Multifractal spectra and multifractal rigidity for horseshoes
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Phase transitions for uniformly expanding maps
• Ergodic theory of parabolic horseshoes
• Rotation, entropy, and equilibrium states
• Equilibrium states for interval maps: the potential $-t\log |Df|$
• Examples for the Nonuniqueness of the Equilibrium State
• Criteria for $\bar {d}$-continuity
• On the variational principle for the topological entropy of certain non-compact sets
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• Thermodynamic formalism for countable Markov shifts
• On the topological entropy of saturated sets
• Phase transitions for countable Markov shifts

This page was built for publication: Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes