LEADER 03065nam 2200493 450 001 9910826961003321 005 20190812132903.0 010 $a1-4704-5247-2 035 $a(CKB)4100000008483125 035 $a(MiAaPQ)EBC5788255 035 $a(PPN)237290871 035 $a(EXLCZ)994100000008483125 100 $a20190627d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric pressure for multimodal maps of the interval /$fFeliks Przytycki, Juan Rivera-Letelier 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (v, 81 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1246 311 $a1-4704-3567-5 320 $aIncludes bibliographical references. 330 $a"This memoir is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. We work in a setting of generalized multimodal maps, that is smooth maps f of a finite union of compact intervals I in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. We prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pullbacks). We prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential - t log |f|, give the same value (including pressure on periodic orbits, "tree" pressure, variational pressures and conformal pressure). Finally we prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the "condensation" and "freezing" parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1246. 606 $aConformal geometry 606 $aMappings (Mathematics) 606 $aRiemann surfaces 615 0$aConformal geometry. 615 0$aMappings (Mathematics) 615 0$aRiemann surfaces. 676 $a514.742 686 $a37E05$a37D25$a37D35$2msc 700 $aPrzytycki$b Feliks$0473482 702 $aRivera-Letelier$b Juan$f1975- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826961003321 996 $aGeometric pressure for multimodal maps of the interval$93958658 997 $aUNINA