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

被引:0
作者
Qiuhong Wang
Yun Zhao
机构
[1] Soochow University,School of Mathematical Sciences
来源
Frontiers of Mathematics in China | 2018年 / 13卷
关键词
Projection pressure; asymptotically (sub)-additive potentials; variational principle; zero temperature limits; 37D35; 37C45; 37B10;
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学科分类号
摘要
Let {Si}i=1l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{S_i\}_{i=1}^l$$\end{document} be an iterated function system (IFS) on ℝd with an attractor K. Let (∑, σ) denote the one-sided full shift over the finite alphabet {1, 2,...,l}, and let π : ∑ → K be the coding map. Given an asymptotically (sub)-additive sequence of continuous functions ℱ = {fn}n⩾1; we define the asymptotically additive projection pressure Pπ(ℱ) and show the variational principle for Pπ(ℱ) under certain affne 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 Pπ(βℱ) with positive parameter β.
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页码:1099 / 1120
页数:21
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