A characterization of hyperbolic potentials of rational maps

DOI10.1007/s00574-012-0007-1zbMath1268.37030arXiv1109.0646OpenAlexW2000056086MaRDI QIDQ1935326

Juan Rivera-Letelier, Irene Inoquio-Renteria

Publication date: 14 February 2013

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.0646

zbMATH Keywords

thermodynamic formalismergodic theorycomplex dynamical systemsnon-uniformly hyperbolic systems

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) 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) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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Cites Work

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• Nice inducing schemes and the thermodynamics of rational maps
• Natural equilibrium states for multimodal maps
• Equilibrium states for interval maps: potentials with \(\sup\varphi- \inf\varphi<h_{\mathrm{top}}(f)\)
• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
• Complex dynamics
• Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
• On thermodynamics of rational maps. I: Negative spectrum
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• The Collet-Eckmann condition for rational functions on the Riemann sphere
• Large deviation principles for non-uniformly hyperbolic rational maps
• On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions
• Complex maps without invariant densities
• An invariant measure for rational maps
• On the uniqueness of the maximizing measure for rational maps
• An inequality for the entropy of differentiable maps
• A Measure Associated with Axiom-A Attractors
• Equilibrium states for S-unimodal maps
• Convergence of the transfer operator for rational maps
• Julia and John
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• Dynamics in One Complex Variable. (AM-160)
• Ergodic theory of equilibrium states for rational maps
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Harmonic measure and expansion on the boundary of the connectedness locus.