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Mosc. Math. J., 2005, Volume 5, Number 3, Pages 669–678 (Mi mmj214)  

This article is cited in 16 scientific papers (total in 16 papers)

Thermodynamical formalism associated with inducing schemes for one-dimensional maps

Ya. B. Pesina, S. Sentib

a Pennsylvania State University
b Instituto Nacional de Matemática Pura e Aplicada

Abstract: For a smooth map $f$ of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions $\varphi$ on I which admit a unique equilibrium measure $\mu_\varphi$. Our results apply to unimodal maps corresponding to a positive Lebesgue measure set of parameters in a one-parameter transverse family.

Key words and phrases: Equilibrium measures, Gibbs measures, inducing schemes, thermodynamic formalism, unimodal maps.

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MSC: 37D25, 37D35, 37E05, 37E10
Received: July 4, 2005
Language: English

Citation: Ya. B. Pesin, S. Senti, “Thermodynamical formalism associated with inducing schemes for one-dimensional maps”, Mosc. Math. J., 5:3 (2005), 669–678

Citation in format AMSBIB
\by Ya.~B.~Pesin, S.~Senti
\paper Thermodynamical formalism associated with inducing schemes for one-dimensional maps
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 3
\pages 669--678

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    This publication is cited in the following articles:
    1. Pesin Ya., Zhang Ke, “Phase transitions for uniformly expanding maps”, J. Stat. Phys., 122:6 (2006), 1095–1110  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Przytycki F., Rivera-Letelier J., “Statistical properties of topological Collet-Eckmann maps”, Ann. Sci. Icole Norm. Sup. (4), 40:1 (2007), 135–178  crossref  mathscinet  zmath  isi  scopus
    3. Pesin Ya., Zhang K., “Thermodynamics of inducing schemes and liftability of measures”, Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow, Fields Institute Communications, 51, 2007, 289–305  mathscinet  zmath  isi
    4. Bruin H., Todd M., “Equilibrium states for interval maps: potentials with $\sup\phi-\inf\phi<h_top(f)$”, Comm. Math. Phys., 283:3 (2008), 579–611  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Pesin Ya., Senti S., “Equilibrium measures for maps with inducing schemes”, J. Mod. Dyn., 2:3 (2008), 397–430  crossref  mathscinet  zmath  isi
    6. Oliveira K., Viana M., “Thermodynamical formalism for robust classes of potentials and non-uniformly hyperbolic maps”, Ergodic Theory Dynam. Systems, 28:2 (2008), 501–533  crossref  mathscinet  zmath  isi  scopus
    7. Pesin Ya.B., Senti S., Zhang K., “Lifting measures to inducing schemes”, Ergodic Theory Dynam. Systems, 28:2 (2008), 553–574  crossref  mathscinet  zmath  isi  scopus
    8. Bruin H., Todd M., “Equilibrium states for interval maps: the potential $-tlog|Df|$”, Ann. Sci. Éc. Norm. Supér. (4), 42:4 (2009), 559–600  crossref  mathscinet  zmath  isi
    9. Leplaideur R., Rios I., “On $t$-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes”, Ergodic Theory Dynam. Systems, 29:6 (2009), 1917–1950  crossref  mathscinet  zmath  isi  scopus
    10. Yuri M., “Entropy production at weak Gibbs measures and a generalized variational principle”, Ergodic Theory Dynam. Systems, 29:4 (2009), 1327–1347  crossref  mathscinet  zmath  isi  scopus
    11. Dobbs N., “Renormalisation-induced phase transitions for unimodal maps”, Comm. Math. Phys., 286:1 (2009), 377–387  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Varandas P., Viana M., “Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps”, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 27:2 (2010), 555–593  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Leplaideur R., “Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian”, Ergodic Theory Dynam Systems, 31:2 (2011), 423–447  crossref  zmath  isi  scopus
    14. Leplaideur R., Oliveira K., Rios I., “Equilibrium states for partially hyperbolic horseshoes”, Ergodic Theory Dynam Systems, 31:1 (2011), 179–195  crossref  mathscinet  zmath  isi  scopus
    15. Pinheiro V., “Expanding measures”, Ann Inst H Poincaré Anal Non Linéaire, 28:6 (2011), 889–939  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Pesin Y., Senti S., Zhang K., “Thermodynamics of Towers of Hyperbolic Type”, Trans. Am. Math. Soc., 368:12 (2016), 8519–8552  crossref  mathscinet  zmath  isi  scopus
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