Coronel, DanielRivera-Letelier, Juan2023-08-222023-08-222015Journal of the European Mathematical SocietyOpen AccessVolume 17, Issue 11, Pages 2725 - 276120151435-9855https://repositorio.unab.cl/xmlui/handle/ria/52730Indexación: ScopusWe 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.enPhase transitionQuadratic familyThermodynamic formalismArtículoAtribución 4.0 Internacional (CC BY 4.0)10.4171/JEMS/569