High-order phase transitions in the quadratic family

  • Daniel Coronel

    Universidad Andres Bello, Santiago, Chile
  • Juan Rivera-Letelier

    Pontifica Universidad Católica de Chile, Santiago, Chile


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 near , before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.

Cite this article

Daniel Coronel, Juan Rivera-Letelier, High-order phase transitions in the quadratic family. J. Eur. Math. Soc. 17 (2015), no. 11, pp. 2725–2761

DOI 10.4171/JEMS/569