DIMENSION ESTIMATES FOR REPELLERS AND EXPANDING MEASURES OF <i>C</i><sup>1</sup> DYNAMICAL SYSTEMS

Juan Wang; Tiantian Liu

doi:10.11948/20210316

2022 Volume 12 Issue 4

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Juan Wang, Tiantian Liu. DIMENSION ESTIMATES FOR REPELLERS AND EXPANDING MEASURES OF C1 DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1496-1516. doi: 10.11948/20210316

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Juan Wang, Tiantian Liu. DIMENSION ESTIMATES FOR REPELLERS AND EXPANDING MEASURES OF C¹ DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1496-1516. doi: 10.11948/20210316

DIMENSION ESTIMATES FOR REPELLERS AND EXPANDING MEASURES OF C¹ DYNAMICAL SYSTEMS

Juan Wang¹,
Tiantian Liu^2, ,

1.
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Longteng Street, 201620 Shanghai, China
2.
Department of mathematics, Soochow University, Shizi Street, 215006 Suzhou, Jiangsu, China

Corresponding author: Email: ttliumath@163.com(T. Liu)
Fund Project: The first author is partially supported by National Natural Science Foundation of China (11871361, 11801395) and the undergraduate training Program for innovation of Shanghai University of Engineering Science (cx2121009)

Abstract

Abstract

In this paper, we first conclude sharp upper and sharp lower bounds of dimensions of a repeller with dominated splitting for C¹ expanding maps, using the techniques in sub-additive and super-additive thermodynamic formalism. Furthermore, we prove a sharp upper bound for the Hausdorff dimension of an expanding measure is given by the unique solution of sub-additive measure-theoretic pressure equation for C¹ local diffeomorphisms.
- Dimension /
- repeller /
- expanding measure /
- topological pressure
MSC: 37C45, 37D35, 37H15

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References

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