Ergodic average of typical orbits and typical functions

Hou, Xiaobo; Lin, Wanshan; Tian, Xueting

doi:10.3934/dcds.2023029

DCDS

2023

DOI: 10.3934/dcds.2023029

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Ergodic average of typical orbits and typical functions

Xiaobo Hou¹,

Wanshan Lin²,

Xueting Tian³

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2024

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Cited by 3 publications

References 25 publications

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On the completely irregular set of maps with the shadowing property

Carvalho,

Coelho,

Salgado

2024

Topology and its Applications

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On the completely irregular set of maps with the shadowing property

Carvalho,

Coelho,

Salgado

2024

Topology and its Applications

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Similarities and differences between specification and non-uniform specification

LIN,

TIAN,

2024

Ergod. Th. Dynam. Sys.

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Pavlov [Adv. Math.295 (2016), 250–270; Nonlinearity32 (2019), 2441–2466] studied the measures of maximal entropy for dynamical systems with weak versions of specification property and found the existence of intrinsic ergodicity would be influenced by the assumptions of the gap functions. Inspired by these, in this article, we study the dynamical systems with non-uniform specification property. We give some basic properties these systems have and give an assumption for the gap functions to ensure the systems have the following five properties: CO-measures are dense in invariant measures; for every non-empty compact connected subset of invariant measures, its saturated set is dense in the total space; ergodic measures are residual in invariant measures; ergodic measures are connected; and entropy-dense. In addition, we will give examples to show the assumption is optimal.

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Lyapunov irregular set of Banach cocycles

Chen,

Zang,

Zou

2023

Nonlinearity

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Let ( Σ M , f ) be a topologically mixing subshift of finite type and let be a Hölder continuous map where B × is the set of invertible elements of a Banach ring B. We prove that either all ergodic measures have the same maximal Lyapunov exponent, or the irregular set is residual in Σ M and has full upper capacity topological entropy of Σ M . We also prove for generic fiber-bunched cocycles, similar statements can be strengthened by considering the Bowen topological entropy.

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Ergodic average of typical orbits and typical functions

Cited by 3 publications

References 25 publications

On the completely irregular set of maps with the shadowing property

On the completely irregular set of maps with the shadowing property

Similarities and differences between specification and non-uniform specification

Lyapunov irregular set of Banach cocycles

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