{"paper":{"title":"Removal of phase transition of the Chebyshev quadratic and thermodynamics of H\\'enon-like maps near the first bifurcation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Hiroki Takahasi","submitted_at":"2016-03-02T06:29:46Z","abstract_excerpt":"We treat a problem at the interface of dynamical systems and equilibrium statistical physics. It is well-known that the geometric pressure function $$t\\in\\mathbb R\\mapsto \\sup_{\\mu}\\left\\{h_\\mu(T_2)-t\\int\\log |dT_2(x)|d\\mu(x)\\right\\}$$ of the Chebyshev quadratic map $T_2(x)=1-2x^2$ $(x\\in\\mathbb R)$ is not differentiable at $t=-1$. We show that this phase transition can be \"removed\", by an arbitrarily small singular perturbation of the map $T_2$ into H\\'enon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to H\\'enon-like dynam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00591","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}