Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 4
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lopes, A.O. and Mengue, J.K. 2014. Selection of measure and a large deviation principle for the general one-dimensionalXYmodel. Dynamical Systems, Vol. 29, Issue. 1, p. 24.


    Lopes, Artur O 1990. Dimension spectra and a mathematical model for phase transition. Advances in Applied Mathematics, Vol. 11, Issue. 4, p. 475.


    Lopes, Artur O. 1989. An analogy of the charge distribution on Julia sets with the Brownian motion. Journal of Mathematical Physics, Vol. 30, Issue. 9, p. 2120.


    Lopes, Artur O. 1989. The Dimension Spectrum of the Maximal Measure. SIAM Journal on Mathematical Analysis, Vol. 20, Issue. 5, p. 1243.


    ×
  • Ergodic Theory and Dynamical Systems, Volume 6, Issue 3
  • September 1986, pp. 393-399

Equilibrium measures for rational maps

  • Artur Oscar Lopes (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700003576
  • Published online: 01 September 2008
Abstract
Abstract

For a polynomial map the measure of maximal entropy is the equilibrium measure for the logarithm potential in the Julia set [1], [4].

Here we will show that in the case where f is a rational map such that f(∞) = ∞ and the Julia set is bounded, then the two measures mentioned above are equal if and only if f is a polynomial.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Equilibrium measures for rational maps
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Equilibrium measures for rational maps
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Equilibrium measures for rational maps
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]M. F. Barnsley , J. S. Geronimo & A. N. Harrington . Orthogonal polynomials associated with invariant measure on the Julia set. Bull. Amer. Math. Soc. 7 (1982).

[2]D. Bessis , D. Mehta & P. Moussa . Orthogonal polynomials on a family of Cantor sets and the problem of iterations of quadratic mappings. Lett. Math. Phys. 6 (1982).

[4]A. Freire , A. Lopes & R. Mane . An invariant measure for rational maps. Bol. Soc. Bras. Mat. 14 (1) (1983).

[6]R. Mañé . On the uniqueness of the maximizing measure for rational maps. Bol.Soc. Bras. Mat. 14 (1) (1983).

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