Geodesic
High-order phase transitions in the quadratic family
Journal of the European Mathematical Society, Tome 17 (2015) no. 11, pp. 2725-2761 Cet article a éte moissonné depuis la source EMS Press

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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=0, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.
DOI : 10.4171/jems/569
Classification : 37-XX
Keywords: Quadratic family, thermodynamic formalism, phase transition 
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     author = {Daniel Coronel and Juan Rivera-Letelier},
     title = {High-order phase transitions in the quadratic family},
     journal = {Journal of the European Mathematical Society},
     pages = {2725--2761},
     year = {2015},
     volume = {17},
     number = {11},
     doi = {10.4171/jems/569},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/569/}
}
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Daniel Coronel; Juan Rivera-Letelier. High-order phase transitions in the quadratic family. Journal of the European Mathematical Society, Tome 17 (2015) no. 11, pp. 2725-2761. doi: 10.4171/jems/569

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