2014, 21: 72-79. doi: 10.3934/era.2014.21.72

From local to global equilibrium states: Thermodynamic formalism via an inducing scheme

1. 

Laboratoire de Mathématiques de Bretagne Atlantique, UMR 6205, Université de Brest, 6, avenue Victor Le Gorgeu, C.S. 93837, France

Received  October 2013 Revised  December 2013 Published  May 2014

We present a method to construct equilibrium states via inducing. This method can be used for some non-uniformly hyperbolic dynamical systems and for non-Hölder continuous potentials. It allows us to prove the existence of phase transition.
Citation: Renaud Leplaideur. From local to global equilibrium states: Thermodynamic formalism via an inducing scheme. Electronic Research Announcements, 2014, 21: 72-79. doi: 10.3934/era.2014.21.72
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show all references

References:
[1]

Stoch. Dyn., 12 (2012), 1250005, 34 pp. doi: 10.1142/S0219493712500050.  Google Scholar

[2]

Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, 1975.  Google Scholar

[3]

Comm. Math. Phys., 321 (2013), 209-247. doi: 10.1007/s00220-012-1651-4.  Google Scholar

[4]

Discrete Contin. Dyn. Syst., 13 (2005), 399-411. doi: 10.3934/dcds.2005.13.399.  Google Scholar

[5]

Ann. of Math. (2), 54 (1951), 595-608. doi: 10.2307/1969491.  Google Scholar

[6]

Trans. Amer. Math. Soc., 228 (1977), 223-241.  Google Scholar

[7]

London Mathematical Society Student Texts, 42, Cambridge University Press, Cambridge, 1998.  Google Scholar

[8]

arXiv:1301.5413, 2013. Google Scholar

[9]

Trans. Amer. Math. Soc., 352 (2000), 1889-1912. doi: 10.1090/S0002-9947-99-02479-4.  Google Scholar

[10]

Nonlinearity, 18 (2005), 2847-2880. doi: 10.1088/0951-7715/18/6/023.  Google Scholar

[11]

Ergodic Theory Dynam. Systems, 31 (2011), 423-447. doi: 10.1017/S0143385709001126.  Google Scholar

[12]

Ergodic Theory Dynam. Systems, 29 (2009), 1917-1950. doi: 10.1017/S0143385708000941.  Google Scholar

[13]

Corrected reprint of the 1983 original, Cambridge Studies in Advanced Mathematics, 2, Cambridge University Press, Cambridge, 1989.  Google Scholar

[14]

Comm. Math. Phys., 74 (1980), 189-197. doi: 10.1007/BF01197757.  Google Scholar

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