On thermodynamics of rational maps. I: Negative spectrum

DOI10.1007/s002200050833zbMath0983.37033OpenAlexW2122921131MaRDI QIDQ1582996

Nikolai Makarov, Stanislav Smirnov

Publication date: 22 October 2000

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050833

zbMATH Keywords

spectruminvariant measurerational mapsmaximal measure

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems involving maps of the interval (37E05)

Related Items (17)

Removal of phase transition in the Chebyshev quadratic and thermodynamics for Hénon-like maps near the first bifurcation ⋮ Building thermodynamics for non-uniformly hyperbolic maps ⋮ Analytic families of semihyperbolic generalized polynomial-like mappings ⋮ A characterization of hyperbolic potentials of rational maps ⋮ Nice inducing schemes and the thermodynamics of rational maps ⋮ Low-temperature phase transitions in the quadratic family ⋮ Geometric pressure for multimodal maps of the interval ⋮ The groupoid \(C^\ast\)-algebra of a rational map ⋮ Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps ⋮ Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles ⋮ Transience and multifractal analysis ⋮ Bowen’s equation in the non-uniform setting ⋮ On the Lyapunov spectrum for rational maps ⋮ Lyapunov spectrum of asymptotically sub-additive potentials ⋮ Renormalisation-induced phase transitions for unimodal maps ⋮ Fixed-point-free elements of iterated monodromy groups ⋮ Porcupine-Like Horseshoes: Topological and Ergodic Aspects

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