On the tail pressure

Yunhua Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2016.025


In this paper, we give two equivalent definitions of tail pressure involving open covers and establish a variational principle which exhibits the relationship between tail pressure and measure-theoretic tail entropy.


Tail pressure; measure-theoretic tail entropy; variational principle

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D. Burguet, A direct proof of the tail variational principle and its extension to maps, Ergodic Theory Dynam. Systems 29 (2009), 357–369.

J. Buzzi, Intrinsic ergodicity for smooth interval maps, Israel J. Math. 100 (1997), 125–161.

Y. Cao, D. Feng and W. Huang, The thermodynamic formalism for sub-additive potentials, Discrete Contin. Dyn. Syst. 20 (2008), no. 3, 639–657.

N. Chung and G. Zhang, Weak expansiveness for actions of sofic groups, J. Funct. Anal. 268 (2015), no. 11, 3534–3565.

T. Downarowicz, Entropy structure, J. Anal. Math. 96 (2005), 57–116.

F. Ledrappier, A variational principle for the topological conditional entropy, Ergodic Theory, Lecture Notes Math. 729, Springer–Verlag, Berlin, 1979, 78–88.

E. Lindenstrauss, Mean dimension, small entropy factors and an embedding theorem, Inst. Hautes Etudes Sci. Publ. Math. 89 (1999), 227–262.

Y. Li, E. Chen and W. Cheng, Tail pressure and the tail entropy function, Ergodic Theory Dynam. Systems 32 (2012), No. 4, 1400–1417.

M. Misiurewicz, Topological conditional entropy, Studia Math. 55 (1976), 176–200. N action on a compact space,

M. Misiurewicz, A short proof of the variational principle for a Z+ Asterique 40 (1976), 147–187.

D. Ruelle, Statistical mechanics on a compact set with Z ν action satisfying expansiveness and specification, Trans. Amer. Math. Soc. 185 (1973), 237–251.

P. Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math. 17 (1976), 937–971.

P. Walters, An Introduction to Ergodic Theory, Spinger, 1982.

G. Zhang, Variational principles of pressure, Discrete Contin. Dyn. Syst. 24 (2009), no. 4, 1409–1435.

Y. Zhou, Tail variational principle for a countable discrete amenable group action, J. Math. Anal. Appl. 433 (2016), no. 2, 1513–1530.

X. Zhou, Y. Zhang and E. Chen, Topological conditional entropy for amenable group actions, Proc. Amer. Math. Soc. 143 (2015), no. 1, 141–150.


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