Rigidity of tame rational functions

• Autorzy: Przytycki F. , Urbański M.
• Języki publikacji: EN

Abstrakty

EN

We introduce and establish some basic properties of the tame rational functions. The class of these functions contains all the rational functions with no recurrent critical points in their Julia sets. For tame non-exceptional functions we prove that the Lipschitz conjugacy, the same spectra of moduli of derivatives at periodic orbits and conformal conjugavcy are mutually equivalent. We prove also the following rigidity result: If h is a Borel measurable invertible map which conjugates two tame functions f and g a.e. and if h transports conformal measure m[sub f] to a measure equivalent to m[sub g] then h extends from a set of full measure m[sub f] to a conformal homeomorphism of neighbourhoods of respective Julia sets. This extends D. Sullivan's rigidity theorem for holomorphic expanding repellers. We provide also a few lines proof of E. Prado's theorem that two generalized polinomial-like maps at zero Teichmueller's distance are holomorphically conjugate.

Słowa kluczowe

EN

Collet-Eckmann maps; conformal conjugacy; conformal measures; holomorphic conjugacy; iteration; Lipschitz conjugacy; Lyapunov spectra; non-linear repellors; non-reccurrent critical points; periodic points; rational functions; repellors; rigidity; Teichmueller distance

PL

analiza całościowa; analiza na rozmaitościach; funkcja wymierna; iteracja; miara konforemna; widmo Lapunowa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 2
• Strony: 163--181
• Opis fizyczny: Bibliogr. 25 poz.,

Twórcy

autor

Przytycki F.

autor

Urbański M.

• Institute of Mathematics, Polish Academy of Science, ul. Śniadeckich 8, 00-950 Warsaw, Poland