High-order phase transitions in the quadratic family

Coronel, Daniel, and Rivera-Letelier, Juan. "High-order phase transitions in the quadratic family." Journal of the European Mathematical Society 017.11 (2015): 2725-2761. <http://eudml.org/doc/277689>.

@article{Coronel2015,
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 $x \mapsto \mathrm \{exp\} (– x^\{–2\})$ near $x = 0$, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.},
author = {Coronel, Daniel, Rivera-Letelier, Juan},
journal = {Journal of the European Mathematical Society},
keywords = {quadratic family; thermodynamic formalism; phase transition; quadratic family; thermodynamic formalism; phase transition},
language = {eng},
number = {11},
pages = {2725-2761},
publisher = {European Mathematical Society Publishing House},
title = {High-order phase transitions in the quadratic family},
url = {http://eudml.org/doc/277689},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Coronel, Daniel
AU - Rivera-Letelier, Juan
TI - High-order phase transitions in the quadratic family
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 11
SP - 2725
EP - 2761
AB - 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 $x \mapsto \mathrm {exp} (– x^{–2})$ near $x = 0$, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.
LA - eng
KW - quadratic family; thermodynamic formalism; phase transition; quadratic family; thermodynamic formalism; phase transition
UR - http://eudml.org/doc/277689
ER -