Abstract
It is well-known that the geometric pressure function (formula presented.) of the Chebyshev quadratic map T2(x) = 1 - 2 x2(x∈ R) is not differentiable at t= - 1. We show that this phase transition can be “removed”, by an arbitrarily small singular perturbation of the map T2 into Hénon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to Hénon-like dynamics near the first bifurcation.
Original language | English |
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Pages (from-to) | 1354-1378 |
Number of pages | 25 |
Journal | Journal of Statistical Physics |
Volume | 164 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2016 Sep 1 |
Keywords
- Chebyshev quadratic map
- Hénon-like maps
- Phase transition
- Thermodynamic formalism
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics