Articles liés à Geometric Pressure for Multimodal Maps of the Interval

Geometric Pressure for Multimodal Maps of the Interval - Couverture souple

Przytycki, Feliks; Rivera-Letelier, Juan

 
9781470435677: Geometric Pressure for Multimodal Maps of the Interval
Couverture souple
ISBN 10 : 1470435675 ISBN 13 : 9781470435677
Editeur : American Mathematical Society, 2019

Synopsis

This paper 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.

The authors work in a setting of generalized multimodal maps, that is, smooth maps $f$ of a finite union of compact intervals $\widehat I$ in $\mathbb{R}$ into $\mathbb{R}$ 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. They 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 pull-backs). They 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 they 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

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

Juan Rivera-Letelier, University of Rochester, NY.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2019
Langue
anglais
ISBN 10 
1470435675
ISBN 13 
9781470435677
Reliure
Broché
Nombre de pages
81
Coordonnées du fabricant
non disponible
Personne responsable
non disponible