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Equality of pressures for rational functions
KTH, Superseded Departments, Mathematics.
2004 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 24, 891-914 p.Article in journal (Refereed) Published
Abstract [en]

We prove that for all rational functions f on the Riemann sphere and potential -t ln \f'\ t greater than or equal to 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.

Place, publisher, year, edition, pages
2004. Vol. 24, 891-914 p.
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URN: urn:nbn:se:kth:diva-44839DOI: 10.1017/S0143385703000385ISI: 000222296200013ScopusID: 2-s2.0-2942704291OAI: diva2:451714
QC 20111026Available from: 2011-10-26 Created: 2011-10-25 Last updated: 2011-10-26Bibliographically approved

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