Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:51:38.040Z Has data issue: false hasContentIssue false
  • English
  • Français

Tail pressure and the tail entropy function

Published online by Cambridge University Press:  14 June 2011

YUAN LI ,
ERCAI CHEN  and
WEN-CHIAO CHENG
YUAN LI
Affiliation:
School of Mathematical Science, Nanjing Normal University, Nanjing 210097, Jiangsu, PR China (email: [email protected], [email protected])
ERCAI CHEN
Affiliation:
School of Mathematical Science, Nanjing Normal University, Nanjing 210097, Jiangsu, PR China (email: [email protected], [email protected]) Center of Nonlinear Science, Nanjing University, Nanjing 210093, Jiangsu, PR China
WEN-CHIAO CHENG
Affiliation:
Department of Applied Mathematics, Chinese Culture University, Yangmingshan, Taipei 11114, Taiwan (email: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Burguet [A direct proof of the tail variational principle and its extension to maps. Ergod. Th. & Dynam. Sys.29 (2009), 357–369] presented a direct proof of the variational principle of tail entropy and extended Downarowicz’s results to a non-invertible case. This paper defines and discusses tail pressure, which is an extension of tail entropy for continuous transformations. This study reveals analogs of many known results of topological pressure. Specifically, a variational principle is provided and some applications of tail pressure, such as the investigation of invariant measures and equilibrium states, are also obtained.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 4 , August 2012 , pp. 1400 - 1417
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Boyle, M. and Downarowicz, T.. The entropy theory of symbolic extension. Invent. Math. 156(1) (2004), 119–161.CrossRefGoogle Scholar
[2]Burguet, D.. A direct proof of the tail variational principle and its extension to maps. Ergod. Th. & Dynam. Sys. 29 (2009), 357–369.CrossRefGoogle Scholar
[3]Bousch, T.. La condition de Walters. Ann. Sci. Éc. Norm. Supér. 34 (2001), 287–311.CrossRefGoogle Scholar
[4]Chazottes, J.-R. and Hochman, M.. On the zero-temperature of Gibbs states. Comm. Math. Phys. 297 (2010), 265–281.CrossRefGoogle Scholar
[5]Downarowicz, T.. Entropy structure. J. Anal. 96 (2005), 57–116.Google Scholar
[6]Downarowicz, T. and Serafin, J.. Fiber entropy and conditional variational principles in compact non-metrizable spaces. Fund. Math. 172 (2002), 217–247.Google Scholar
[7]Huang, W. and Ye, X.. A local variational relation and applications. Israel J. Math. 151 (2006), 237–279.CrossRefGoogle Scholar
[8]Huang, W., Ye, X. and Zhang, G.. A local variational principle for conditional entropy. Ergod. Th. & Dynam. Sys. 26(1) (2006), 219–245.CrossRefGoogle Scholar
[9]Huang, X., Wen, X. and Zeng, F.. Topological pressure of non-automomous dynamical systems. Nonlinear Dyn. Syst. Theory 8(1) (2008), 43–48.Google Scholar
[10]Huang, W. and Yi, Y.. A local variational principle of pressure and its applications to equilibrium states. Israel J. Math. 161(1) (2007), 29–74.CrossRefGoogle Scholar
[11]Katok, A. and Hasselblatt, B.. An Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications, 54). Cambridge University Press, Cambridge, 1995.Google Scholar
[12]Lindenstrauss, E.. Mean dimension, small entropy factors and an embedding theorem. Publ. Math. Inst. Hautes Études Sci. 89 (1999), 227–262.CrossRefGoogle Scholar
[13]Misiurewicz, M.. Topological conditional entropy. Studia Math. 55 (1976), 175–200.CrossRefGoogle Scholar
[14]Morris, I. D.. The Mañé–Conze–Guivarc’h lemma for intermittent maps of the circle. Ergod. Th. & Dynam. Sys. 29 (2009), 1603–1611.CrossRefGoogle Scholar
[15]Morris, I. D.. Ergodic optimization for generic continuous functions. Discrete Contin. Dyn. Syst. 27 (2010), 383–388.CrossRefGoogle Scholar
[16]Pesin, Ya.. Dimension type characteristics for invariant sets of dynamical systems. Russian Math. Surveys 43(4) (1988), 111–151.CrossRefGoogle Scholar
[17]Pesin, Ya. and Pitskel, B.. Topological pressure and the variational principle for non-compact sets. Funct. Anal. Appl. 18 (1984), 307–318.CrossRefGoogle Scholar
[18]Pollner, P. and Vattay, G.. New method for computing topological pressure. Phys. Rev. Lett. 76(22) (1996), 4155–4163.CrossRefGoogle ScholarPubMed
[19]Romagnoli, P. P.. A local variational principle for the topological entropy. Ergod. Th. & Dynam. Sys. 23 (2003), 1601–1610.CrossRefGoogle Scholar
[20]Walters, P.. An Introduction to Ergodic Theory. Springer, New York, 1982.CrossRefGoogle Scholar