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Geometric Pressure for Multimodal Maps of the Interval (Memoirs of the American Mathematical Society, Band 259) - Softcover

Przytycki, Feliks; Rivera-letelier, Juan

 
9781470435677: Geometric Pressure for Multimodal Maps of the Interval (Memoirs of the American Mathematical Society, Band 259)
Softcover
ISBN 10: 1470435675 ISBN 13: 9781470435677
Verlag: American Mathematical Society, 2019

Inhaltsangabe

"This memoir is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. We work in a setting of generalized multimodal maps, that is smooth maps f of a finite union of compact intervals I in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. We prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pullbacks). We prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential - t log |f|, give the same value (including pressure on periodic orbits, "tree" pressure, variational pressures and conformal pressure). Finally we prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the "condensation" and "freezing" parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties"--

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Über die Autorin bzw. den Autor

Feliks Przytycki, Polish Academy of Sciences, Warszawa, Poland.

Juan Rivera-Letelier, University of Rochester, NY.

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Verlag
American Mathematical Society
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
1470435675
ISBN 13 
9781470435677
Einband
Taschenbuch
Anzahl der Seiten
81
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Verantwortliche Person
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