SUB-ADDITIVE PRESSURE ON A BOREL SET

doi:10.1016/S0252-9602(15)30049-7

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1203-1213.doi: 10.1016/S0252-9602(15)30049-7

SUB-ADDITIVE PRESSURE ON A BOREL SET

陈阳洋¹, 赵云¹, 郑文巧²

1. Department of Mathematics, Soochow University, Suzhou 215006, China;
2. Department of Applied Mathematics, Chinese Culture University Yangmingshan, Taipei 11114, China

收稿日期:2013-07-23 修回日期:2014-10-24 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Wen-Chiao CHENG E-mail:zwq2@faculty.pccu.edu.tw
作者简介:Yangyang CHEN, E-mail: oufei861155909@163.com; E-mail: zhaoyun@suda.edu.cn; Yun ZHAO, Wen-Chiao CHENG, E-mail: zwq2@faculty.pccu.edu.tw
基金资助:
For this research, Chen was partially supported by National University Student Innovation Program (111028508). Cheng was supported by NSC Grant NSC 101-2115-M-034-001. Zhao was partially supported by NSFC (11371271). This work was partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

SUB-ADDITIVE PRESSURE ON A BOREL SET

Yangyang CHEN¹, Yun ZHAO¹, Wen-Chiao CHENG²

1. Department of Mathematics, Soochow University, Suzhou 215006, China;
2. Department of Applied Mathematics, Chinese Culture University Yangmingshan, Taipei 11114, China

Received:2013-07-23 Revised:2014-10-24 Online:2015-09-01 Published:2015-09-01
Contact: Wen-Chiao CHENG E-mail:zwq2@faculty.pccu.edu.tw
Supported by:
For this research, Chen was partially supported by National University Student Innovation Program (111028508). Cheng was supported by NSC Grant NSC 101-2115-M-034-001. Zhao was partially supported by NSFC (11371271). This work was partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

摘要/Abstract

摘要：

The goal of this paper is to investigate topological conditional pressure of a continuous transformation as defined for sub-additive potentials. This study presents a variational inequality for sub-additive topological conditional pressure on a closed subset, which is the other form of the variational principle for the sub-additive topological pressure presented by Cao, Feng, and Huang in [9]. Moreover, under some additional assumptions, this result can be generalized to the non-compact case.

关键词: sub-additive potentials, topological pressure, conditional entropy, variational inequality

Abstract:

Key words: sub-additive potentials, topological pressure, conditional entropy, variational inequality

中图分类号:

37A30

陈阳洋, 赵云, 郑文巧. SUB-ADDITIVE PRESSURE ON A BOREL SET[J]. 数学物理学报(英文版), 2015, 35(5): 1203-1213.

Yangyang CHEN, Yun ZHAO, Wen-Chiao CHENG. SUB-ADDITIVE PRESSURE ON A BOREL SET[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1203-1213.

参考文献

[1] Adler R L, Konheim A G, McAndrew M H. Topological entropy. Trans Amer Math Soc, 1965, 114:309-319
[2] Ban Jungchao, Cao Yongluo, Hu Huyi. Dimensions of average conformal repeller and average. Trans Amer Math Soc, 2010, 362:727-751
[3] Barreira L M. A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems. Ergod Th Dynam Syst, 1996, 16:871-927
[4] Barreira L M. Dimension and recurrence in hyperbolic dynamics//Progress in Mathematics, 272. Basel:Birkhäuser Verlag, 2008
[5] Barreira L. Nonadditive thermodynamic formalism:equilibrium and Gibbs measures. Disc Contin Dyn Syst, 2006, 16:279-305
[6] Barreira L. Almost additive thermodynamic formalism:some recent developments. Rev Math Phys, 2010, 22(10):1147-1179
[7] Bowen R. Topological entropy for noncompact sets. Trans Amer Math Soc, 1973, 184:125-136
[8] Bowen R. Equilibrium states and the ergodic theory of Anosov diffeomorphism//Lecture Notes in Math, Vol 470. New York:Springer-Verlag, 1975
[9] Cao Y, Feng D, Huang W. The thermodynamic formalism for sub-additive potentials. Disc Contin Dyn Sys, 2008, 20(3):639-657
[10] Cheng W. Estimate for supremum of conditional entropy on a closed subset. Taiwanese J Math, 2008, 12(7):1791-1803
[11] Falconer K J. A subadditive thermodynamic formalism for mixing repellers. J Phys A, 1988, 21(14):L737-L742
[12] Feng D, Huang W. Lyapunov spectrum of asymptotically sub-additive potentials. Commun Math Phys, 2010, 297:1-43
[13] Gelfert K. Equality of pressures for diffeomorphisms preserving hyperbolic measures. Math Z, 2009, 261(4):711-724
[14] Gelfert K, Wolf C. Topological pressure via saddle points. Trans Amer Math Soc, 2008, 360(1):545-561
[15] Li Y, Chen E, Cheng W. Variational inequality for conditional pressure on a Borel subset. Pacific J Math, 2012, 256(1):151-164
[16] Huang W, Yi Y. A local variational principle of pressure and its applications to equilibrium states. Israel J Math, 2007, 161:29-94
[17] Molaeo M R. Dynamically defined topological pressure. J Dyn Syst Geom Theor, 2008, 6(1):75-81
[18] Mummert A. The thermodynamic formalism for almost-additive sequences. Discrete Contin Dyn Syst, 2006, 16:435-454
[19] Pesin Y, Pitskel B. Topological pressure and the variational principle for noncompact sets. Funct Anal Appl, 1984, 18:307-318
[20] Pesin Y. Dimension Theory in Dynamical Systems, Contemporary Views and Applications. Chicago:University of Chicago Press, 1997
[21] Ruelle D. Statistical mechanics on a compact set with Z^v action satisfying expansiveness and specification. Trans Ame Math Soc, 1973, 187:237-251
[22] Walters P. A variational principle for the pressure of continuous transformations. Amer J Math, 1975, 97(4):937-971
[23] Walters P. An Introduction to Ergodic Theory. Berlin, Heidelberg, New York:Springer-Verlag, 1982
[24] Zhang G. Variational principles of pressure. Dis Contin Dyn Syst, 2009, 24(4):1409-1435
[25] Zhao Y, Cheng W. Variational principle for conditional pressure with subadditive potential. Open Syst Inf Dyn, 2011, 18(4):389-404
[26] Zhao Y, Cheng W. Coset pressure with sub-additive potentials. Stoch Dyn, 2014, 14(1):1350012

SUB-ADDITIVE PRESSURE ON A BOREL SET

SUB-ADDITIVE PRESSURE ON A BOREL SET

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