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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 |
References:
[1] |
A. Baraviera, R. Leplaideur and A. O. Lopes, The potential point of view for renormalization, Stoch. Dyn., 12 (2012), 1250005, 34 pp.
doi: 10.1142/S0219493712500050. |
[2] |
R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, 1975. |
[3] |
H. Bruin and R. Leplaideur, Renormalization, thermodynamic formalism and quasi-crystals in subshifts, Comm. Math. Phys., 321 (2013), 209-247.
doi: 10.1007/s00220-012-1651-4. |
[4] |
J.-R. Chazottes and R. Leplaideur, Fluctuations of the $N$th return time for Axiom A diffeomorphisms, Discrete Contin. Dyn. Syst., 13 (2005), 399-411.
doi: 10.3934/dcds.2005.13.399. |
[5] |
Y. N. Dowker, Finite and $\sigma$-finite invariant measures, Ann. of Math. (2), 54 (1951), 595-608.
doi: 10.2307/1969491. |
[6] |
F. Hofbauer, Examples for the nonuniqueness of the equilibrium state, Trans. Amer. Math. Soc., 228 (1977), 223-241. |
[7] |
G. Keller, Equilibrium States in Ergodic Theory, London Mathematical Society Student Texts, 42, Cambridge University Press, Cambridge, 1998. |
[8] |
R. Leplaideur, Chaos: Butterflies also generate phase transitions and parallel universes, arXiv:1301.5413, 2013. |
[9] |
R. Leplaideur, Local product structure for equilibrium states, Trans. Amer. Math. Soc., 352 (2000), 1889-1912.
doi: 10.1090/S0002-9947-99-02479-4. |
[10] |
R. Leplaideur, A dynamical proof for the convergence of Gibbs measures at temperature zero, Nonlinearity, 18 (2005), 2847-2880.
doi: 10.1088/0951-7715/18/6/023. |
[11] |
R. Leplaideur, Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian, Ergodic Theory Dynam. Systems, 31 (2011), 423-447.
doi: 10.1017/S0143385709001126. |
[12] |
R. Leplaideur and I. Rios, On $t$-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes, Ergodic Theory Dynam. Systems, 29 (2009), 1917-1950.
doi: 10.1017/S0143385708000941. |
[13] |
K. Petersen, Ergodic Theory, Corrected reprint of the 1983 original, Cambridge Studies in Advanced Mathematics, 2, Cambridge University Press, Cambridge, 1989. |
[14] |
Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys., 74 (1980), 189-197.
doi: 10.1007/BF01197757. |
show all references
References:
[1] |
A. Baraviera, R. Leplaideur and A. O. Lopes, The potential point of view for renormalization, Stoch. Dyn., 12 (2012), 1250005, 34 pp.
doi: 10.1142/S0219493712500050. |
[2] |
R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, 1975. |
[3] |
H. Bruin and R. Leplaideur, Renormalization, thermodynamic formalism and quasi-crystals in subshifts, Comm. Math. Phys., 321 (2013), 209-247.
doi: 10.1007/s00220-012-1651-4. |
[4] |
J.-R. Chazottes and R. Leplaideur, Fluctuations of the $N$th return time for Axiom A diffeomorphisms, Discrete Contin. Dyn. Syst., 13 (2005), 399-411.
doi: 10.3934/dcds.2005.13.399. |
[5] |
Y. N. Dowker, Finite and $\sigma$-finite invariant measures, Ann. of Math. (2), 54 (1951), 595-608.
doi: 10.2307/1969491. |
[6] |
F. Hofbauer, Examples for the nonuniqueness of the equilibrium state, Trans. Amer. Math. Soc., 228 (1977), 223-241. |
[7] |
G. Keller, Equilibrium States in Ergodic Theory, London Mathematical Society Student Texts, 42, Cambridge University Press, Cambridge, 1998. |
[8] |
R. Leplaideur, Chaos: Butterflies also generate phase transitions and parallel universes, arXiv:1301.5413, 2013. |
[9] |
R. Leplaideur, Local product structure for equilibrium states, Trans. Amer. Math. Soc., 352 (2000), 1889-1912.
doi: 10.1090/S0002-9947-99-02479-4. |
[10] |
R. Leplaideur, A dynamical proof for the convergence of Gibbs measures at temperature zero, Nonlinearity, 18 (2005), 2847-2880.
doi: 10.1088/0951-7715/18/6/023. |
[11] |
R. Leplaideur, Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian, Ergodic Theory Dynam. Systems, 31 (2011), 423-447.
doi: 10.1017/S0143385709001126. |
[12] |
R. Leplaideur and I. Rios, On $t$-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes, Ergodic Theory Dynam. Systems, 29 (2009), 1917-1950.
doi: 10.1017/S0143385708000941. |
[13] |
K. Petersen, Ergodic Theory, Corrected reprint of the 1983 original, Cambridge Studies in Advanced Mathematics, 2, Cambridge University Press, Cambridge, 1989. |
[14] |
Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys., 74 (1980), 189-197.
doi: 10.1007/BF01197757. |
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