# High-order phase transitions in the quadratic family

Daniel Coronel; Juan Rivera-Letelier

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 11, page 2725-2761
- ISSN: 1435-9855

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topCoronel, 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 -

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