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Highlights
In equilibrium statistical physics, originated by Boltzmann (1877) and Gibbs (1902), the Ising model of ferromagnetism is considered
≈ (diam fx−n(B(f n(x), r0)))t exp(−nP). The latter follows from a comparison of the diameter with the inverse of the absolute value of the derivative of f n at x, due to bounded distortion
C2 is called.a generalized multimodal map if it is defined on a neighbourhood of a compact invariant set K, critical points are not infinitely flat, bounded distortion (BD) property for iterates holds, is topologically transitive, and has positive topological entropy on K
Summary
In equilibrium statistical physics, originated by Boltzmann (1877) and Gibbs (1902), the Ising model of ferromagnetism is considered. Let f : X → X be a distance expanding, topologically transitive continuous open map of a compact metric space X and φ : X → R be a Hölder continuous potential. For f real of class C1+ε or f holomorphic (conformal) for an expanding repeller X, considering φ = φt := −t log |f | for t ∈ R, the Gibbs property gives, as exp Sn(φt) = |(f n) |−t, μφt (fx−n(B(f n(x), r0))) ≈ exp(Snφ(x) − nP (φt)). C2 is called.a generalized multimodal map if it is defined on a neighbourhood of a compact invariant set K, critical points are not infinitely flat, bounded distortion (BD) property for iterates holds, is topologically transitive, and has positive topological entropy on K. being the mated with rabbit boundary between white (basilica) and black (rabbit), Sierpiński-Julia carpet f (z) =. Basic sets in spectral decomposition via renormalizations [3, Theorem III.4.2]
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