03065nam 2200493 450 991079361950332120190812132903.01-4704-5247-2(CKB)4100000008483125(MiAaPQ)EBC5788255(PPN)237290871(EXLCZ)99410000000848312520190627d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric pressure for multimodal maps of the interval /Feliks Przytycki, Juan Rivera-LetelierProvidence, Rhode Island :American Mathematical Society,[2019]©20191 online resource (v, 81 pages)Memoirs of the American Mathematical Society ;Volume 259, Number 12461-4704-3567-5 Includes bibliographical references."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"--Provided by publisher.Memoirs of the American Mathematical Society ;Volume 259, Number 1246.Conformal geometryMappings (Mathematics)Riemann surfacesConformal geometry.Mappings (Mathematics)Riemann surfaces.514.74237E0537D2537D35mscPrzytycki Feliks473482Rivera-Letelier Juan1975-MiAaPQMiAaPQMiAaPQBOOK9910793619503321Geometric pressure for multimodal maps of the interval3812950UNINA