Irregular sets of two-sided Birkhoff averages and hyperbolic sets

DOI10.1007/S11512-015-0214-2zbMath1361.37009OpenAlexW2206703355MaRDI QIDQ283968

Jinjun Li, Luis Barreira, Claudia Valls

Publication date: 17 May 2016

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11512-015-0214-2

zbMATH Keywords

Markov chainsBirkhoff averagesShannon-McMillan-Breiman theoremsingleton

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Ergodic theorems, spectral theory, Markov operators (37A30) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems with hyperbolic orbits and sets (37D05)

Related Items (4)

Abundance of wild historic behavior ⋮ On exceptional sets in Erdős-Rényi limit theorem revisited ⋮ The asymptotically additive topological pressure: variational principle for non-compact and intersection of irregular sets ⋮ A note on the distribution of the digits in Cantor expansions

Cites Work

• Ergodic theory, hyperbolic dynamics and dimension theory
• Ergodic limits on the conformal repellers
• Dimension and recurrence in hyperbolic dynamics
• Topological pressure and the variational principle for noncompact sets
• On the distribution of long-term time averages on symbolic space
• Divergence points in systems satisfying the specification property
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• RECURRENCE, DIMENSION AND ENTROPY
• The irregular set for maps with the specification property has full topological pressure
• Topological entropy for divergence points
• A complement to Young's theorem on measure dimension: the difference between lower and upper pointwise dimensions
• Multifractal analysis of hyperbolic flows

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