Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces

DOI10.1007/s00605-014-0605-7zbMath1343.37037OpenAlexW1988428517WikidataQ59397738 ScholiaQ59397738MaRDI QIDQ2449429

Michał Szostakiewicz, Mariusz Urbański, Anna Zdunik

Publication date: 8 May 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-014-0605-7

zbMATH Keywords

Julia setscentral limit theoremequilibrium stateslaw of iterated logarithmexponential decay of correlationstopological pressureholomorphic dynamicscomplex projective spacesPerron-Frobenius operatorsHölder continuous potentials

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodicity, mixing, rates of mixing (37A25) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (5)

Dynamical mechanism behind ghosts unveiled in a map complexification ⋮ Fine inducing and equilibrium measures for rational functions of the Riemann sphere ⋮ Every complex Hénon map is exponentially mixing of all orders and satisfies the CLT ⋮ Equilibrium states of endomorphisms of \(\mathbb{P}^k\). I: Existence and properties ⋮ Thin annuli property and exponential distribution of return times for weakly Markov systems

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