The asymptotically additive topological pressure on the irregular set for asymptotically additive potentials

DOI10.1016/j.na.2011.04.065zbMath1219.37028OpenAlexW2044151102MaRDI QIDQ549938

Yun Zhao, Yong-Luo Cao, Li-bo Zhang

Publication date: 19 July 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.04.065

zbMATH Keywords

variational principlemultifractal analysistopological pressure

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Related Items

Emergence via non-existence of averages ⋮ Variational Principle for Conditional Pressure with Subadditive Potential ⋮ Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure ⋮ Constrained ergodic optimization for asymptotically additive potentials ⋮ Weak Gibbs measures as Gibbs measures for asymptotically additive sequences ⋮ Weak Gibbs measures: speed of convergence to entropy, topological and geometrical aspects ⋮ Pressures for flows on arbitrary subsets ⋮ Q-entropy for general topological dynamical systems ⋮ Highly irregular orbits for subshifts of finite type: large intersections and emergence ⋮ COSET PRESSURE WITH SUB-ADDITIVE POTENTIALS ⋮ The asymptotically additive topological pressure: variational principle for non-compact and intersection of irregular sets ⋮ Topological pressure and large deviations for multivariate potentials ⋮ Additive, almost additive and asymptotically additive potential sequences are equivalent ⋮ Weak specification properties and large deviations for non-additive potentials

Cites Work

• Unnamed Item
• Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures
• The thermodynamic formalism for almost-additive sequences
• Almost additive multifractal analysis
• The thermodynamic formalism for sub-additive potentials
• Dimension and recurrence in hyperbolic dynamics
• Lyapunov spectrum of asymptotically sub-additive potentials
• Measure-theoretic pressure for subadditive potentials
• Topological pressure and the variational principle for noncompact sets
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Multifractal analysis of local entropies for expansive homeomorphisms with specification
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• The Hausdorff dimension of average conformal repellers under random perturbation
• The irregular set for maps with the specification property has full topological pressure
• Dimension spectra of almost additive sequences
• On the variational principle for the topological entropy of certain non-compact sets
• A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems
• The dimensions of a non-conformal repeller and an average conformal repeller
• Topological entropy for divergence points