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Abstrakty
We prove that each non-parabolic periodic orbit contained in the omega-limit set of a measure-recurrent, optimal orbit for a continuous function defined on the Julia set of a non-recurrent rational function is also optimal. As a by-product, we prove in the next section appropriate versions of shadowing and closing lemmas for non-recurrent rational functions.
Wydawca
Rocznik
Tom
Strony
175--184
Opis fizyczny
Bibliogr. 5 poz.
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autor
- Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, USA, urbanski@unt.edu
Bibliografia
- [1] R. Mané, On a theorem of Fatou, Bol. Soc. Brasil. Mat., 24 (1933) 1-11.
- [2] M. Urbański, Rational functions with no recurrent critical points, Ergodic. Theory Dynam. Systems, 14 (1994) 391-414.
- [3] M. Urbański, Geometry and ergodic theory of conformal nonrecurrent dynamics, Ergodic. Theory Dynam. Systems, 17 (1997) 1449-1476.
- [4] M. Urbański, Thermodynamic formalism, topological pressure and escape rates for non-recurrent conformal dynamics, preprint 2000; Fund. Math., to appear.
- [5] G. Yuan, B. Hunt, Optimal orbits of hyperbolic systems, Nonlinearity, 12 (1999) 1207-1224.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0001-0059