Geometric pressure for multimodal maps of the interval / / Feliks Przytycki, Juan Rivera-Letelier

• Autore: Przytycki Feliks
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2019]; ©2019
• Descrizione fisica: 1 online resource (v, 81 pages)
• Disciplina: 514.742
• Soggetto topico: Conformal geometry; Mappings (Mathematics); Riemann surfaces
• Classificazione: 37E0537D2537D35
• Persona (resp. second.): Rivera-LetelierJuan <1975->
• Nota di bibliografia: Includes bibliographical references.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Geometric pressure for multimodal maps of the interval
• ISBN: 1-4704-5247-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910793619503321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 259, Number 1246.