Large deviations and the distribution of pre-images of rational maps

DOI10.1007/BF02101295zbMath0919.30020OpenAlexW2074060852MaRDI QIDQ679397

Mark Pollicott, Richard Sharp

Publication date: 16 August 1999

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

Full work available at URL: https://doi.org/10.1007/bf02101295

zbMATH Keywords

entropyiterationpressureequilibriumJulia setinvariant measuredeviation

Mathematics Subject Classification ID

Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)

Related Items (10)

Statistical properties of periodic points for infinitely renormalizable unimodal maps ⋮ Distribution of typical orbits for random dynamics generated by finitely many rational maps ⋮ Uniqueness of minimizer for countable Markov shifts and equidistribution of periodic points ⋮ Weak expansion properties and large deviation principles for expanding Thurston maps ⋮ Global normal form and asymptotic spectral gap for open partially expanding maps ⋮ Large deviation principles for non-uniformly hyperbolic rational maps ⋮ Statistics in conjugacy classes in free groups ⋮ Quantitative uniform distribution of points of small height on the projective line ⋮ Large Deviation Results for Periodic Points of a Rational Map ⋮ Large deviation principles of one-dimensional maps for Hölder continuous potentials

Cites Work

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• Rational iteration: complex analytic dynamical systems
• On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions
• Entropy and large deviation
• An invariant measure for rational maps
• On the uniqueness of the maximizing measure for rational maps
• Invariant subsets of expanding mappings of the circle
• Ergodic theory of equilibrium states for rational maps

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