Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure

doi:10.1007/s11464-018-0720-1

Front. Math. China

2018, Vol. 13

Issue (5) : 1099-1120 https://doi.org/10.1007/s11464-018-0720-1

RESEARCH ARTICLE

Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure

Qiuhong WANG, Yun ZHAO(

)

School of Mathematical Sciences, Soochow University, Suzhou 215006, China

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Abstract

Let ${S i} i = 1 l$ be an iterated function system (IFS) on $? d$ with an attractor K. Let (Σ, σ) denote the one-sided full shift over the finite alphabet {1, 2, . . . , l}, and let π: Σ → K be the coding map. Given an asymptotically (sub)-additive sequence of continuous functions $F = {f n} n ≥ 1$ , we define the asymptotically additive projection pressure P_π( $F$ ) and show the variational principle for P_π( $F$ ) under certain affine IFS. We also obtain variational principle for the asymptotically sub-additive projection pressure if the IFS satisfies asymptotically weak separation condition (AWSC). Furthermore, when the IFS satisfies AWSC, we investigate the zero temperature limits of the asymptotically sub-additive projection pressure P_π(β $F$ ) with positive parameter β.

Keywords Projection pressure asymptotically (sub)-additive potentials variational principle zero temperature limits

Corresponding Author(s): Yun ZHAO

Issue Date: 29 October 2018

Cite this article:

Qiuhong WANG,Yun ZHAO. Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure[J]. Front. Math. China, 2018, 13(5): 1099-1120.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0720-1
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I5/1099

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