Geometric pressure for multimodal maps of the interval / Feliks Przytycki, Juan Rivera-Letelier.
| Author/creator | Przytycki, Feliks |
| Other author | Rivera-Letelier, Juan, 1975- |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, [2019] |
| Description | v, 81 pages : illustrations ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; volume 259, number 1246 |
| Abstract | "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 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 and the potential - t log 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. |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2019023423 |
| ISBN | 9781470435677 (paperback) |
| ISBN | (pdf) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |