The limit map of a homomorphism of discrete Möbius groups
Pekka Tukia (1995)
Publications Mathématiques de l'IHÉS
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Pekka Tukia (1995)
Publications Mathématiques de l'IHÉS
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Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Manfred Denker, R. Mauldin, Z. Nitecki, Mariusz Urbański (1998)
Fundamenta Mathematicae
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We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.
Vadim A. Kaimanovich (1990)
Annales de l'I.H.P. Physique théorique
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Feliks Przytycki, Juan Rivera-Letelier (2007)
Annales scientifiques de l'École Normale Supérieure
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Mrinal Kanti Roychowdhury (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.
James Fickett, Jan Mycielski (1979)
Colloquium Mathematicae
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Anthony Quas (1999)
Studia Mathematica
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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for or expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Käenmäki, Antti (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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