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High-order phase transitions in the quadratic family

Daniel Coronel, Juan Rivera-Letelier (2015)

Journal of the European Mathematical Society

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.

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