Optimal periodic orbits for non-recurrent rational functions

• Autorzy: Urbański M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

non-recurrent rational functions; optimal orbits; critical points; pseudo-orbits; shadowing lemma; periodic orbits

PL

orbita optymalna; punkt krytyczny; pseudo-orbita; orbita okresowa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 2
• Strony: 175--184
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Urbański M.

• Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, USA,

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.