High-order phase transitions in the quadratic family
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Date
2015
Authors
Profesor/a GuÃa
Facultad/escuela
Idioma
en
Journal Title
Journal ISSN
Volume Title
Publisher
European Mathematical Society Publishing House
Nombre de Curso
item.page.dc.rights
Atribución 4.0 Internacional (CC BY 4.0)
item.page.dc.rights
https://creativecommons.org/licenses/by/4.0/deed.es
Abstract
We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, we show that this phase transition resembles a Kosterlitz-Thouless singularity: Near the critical parameter the geometric pressure function behaves as x → exp.x-2/ near x D 0, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense. © 2015 European Mathematical Society.
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Indexación: Scopus
Keywords
Phase transition, Quadratic family, Thermodynamic formalism
Citation
Journal of the European Mathematical SocietyOpen AccessVolume 17, Issue 11, Pages 2725 - 27612015
DOI
10.4171/JEMS/569