Pre-image variational principle for bundle random dynamical systems
Xianfeng Ma Ercai Chen
The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.
keywords: Pre-image topological pressure Random dynamical systems Variational principle
Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems
Zheng Yin Ercai Chen
This article is devoted to the study of the irregular sets of Birkhoff averages in some nonuniformly hyperbolic systems via Pesin theory. Particularly, we give a conditional variational principle for the topological entropy of the irregular sets. Our result can be applied (i) to the diffeomorphisms on surfaces, (ii) to the nonuniformly hyperbolic diffeomorphisms described by Katok.
keywords: Pesin set Irregular set topological entropy.
On large deviations for amenable group actions
Dongmei Zheng Ercai Chen Jiahong Yang
By proving an amenable version of Katok's entropy formula and handling the quasi tiling techniques, we establish large deviations bounds for countable discrete amenable group actions. This generalizes the classical results of Lai-Sang Young [21].
keywords: Large deviation specification amenable group quasi tiling. entropy

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