Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Huaibin and Rivera-Letelier, Juan 2014. Equilibrium States of Weakly Hyperbolic One-Dimensional Maps for Hölder Potentials. Communications in Mathematical Physics, Vol. 328, Issue. 1, p. 397.


    Zhao, Yun Cao, Yongluo and Wang, Juan 2014. Dimension estimates in non-conformal setting. Discrete and Continuous Dynamical Systems, Vol. 34, Issue. 9, p. 3847.


    Coronel, Daniel and Rivera-Letelier, Juan 2013. Low-temperature phase transitions in the quadratic family. Advances in Mathematics, Vol. 248, p. 453.


    Rivera-Letelier, Juan and Shen, Weixiao 2013. On Poincaré Series of Unicritical Polynomials at the Critical Point. Communications in Mathematics and Statistics, Vol. 1, Issue. 1, p. 1.


    BARAŃSKI, KRZYSZTOF KARPIŃSKA, BOGUSŁAWA and ZDUNIK, ANNA 2012. Bowen’s formula for meromorphic functions. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 04, p. 1165.


    CLIMENHAGA, VAUGHN 2011. Bowen’s equation in the non-uniform setting. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 04, p. 1163.


    COMMAN, HENRI and RIVERA-LETELIER, JUAN 2011. Large deviation principles for non-uniformly hyperbolic rational maps. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 02, p. 321.


    Przytycki, Feliks and Rivera-Letelier, Juan 2011. Nice Inducing Schemes and the Thermodynamics of Rational Maps. Communications in Mathematical Physics, Vol. 301, Issue. 3, p. 661.


    Gelfert, Katrin Przytycki, Feliks and Rams, Michał 2010. On the Lyapunov spectrum for rational maps. Mathematische Annalen, Vol. 348, Issue. 4, p. 965.


    Dobbs, Neil 2009. Renormalisation-Induced Phase Transitions for Unimodal Maps. Communications in Mathematical Physics, Vol. 286, Issue. 1, p. 377.


    INGLE, WILLIAM KAUFMANN, JACIE and WOLF, CHRISTIAN 2009. Natural invariant measures, divergence points and dimension in one-dimensional holomorphic dynamics. Ergodic Theory and Dynamical Systems, Vol. 29, Issue. 04, p. 1235.


    ×

Equality of pressures for rational functions

  • FELIKS PRZYTYCKI (a1), JUAN RIVERA-LETELIER (a2) and STANISLAV SMIRNOV (a3)
  • DOI: http://dx.doi.org/10.1017/S0143385703000385
  • Published online: 01 May 2004
Abstract

We prove that for all rational functions f on the Riemann sphere and potential $-t\ln|f'|, t\ge 0$ all the notions of pressure introduced in Przytycki (Proc. Amer. Math. Soc.351(5) (1999), 2081–2099) coincide. In particular, we get a new simple proof of the equality between the hyperbolic Hausdorff dimension and the minimal exponent of conformal measure on a Julia set. We prove that these pressures are equal to the pressure defined with the use of periodic orbits under an assumption that there are not many periodic orbits with Lyapunov exponent close to 1 moving close together, in particular under the Topological Collet–Eckmann condition. In Appendix A, we discuss the case t < 0.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax