On the work of Sarig on countable Markov chains and thermodynamic formalism

DOI10.3934/jmd.2014.8.1zbMath1351.37150arXiv1301.3917OpenAlexW3102801028WikidataQ56602640 ScholiaQ56602640MaRDI QIDQ478783

Ya. B. Pesin, Tien-Cuong Dinh, Nessim Sibony

Publication date: 4 December 2014

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3917

zbMATH Keywords

Markov chainsthermodynamic formalismJulia setNevanlinna theoryHénon mapholomorphic automorphismGreen currentBrin prizeSarig

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) 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) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Value distribution theory in higher dimensions (32H30)

Related Items (20)

Rigidity of Julia sets of families of biholomorphic mappings in higher dimensions ⋮ Exponential mixing property for Hénon–Sibony maps of ⋮ Equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb C^k\) ⋮ Building thermodynamics for non-uniformly hyperbolic maps ⋮ Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy ⋮ A rigidity theorem for Hénon maps ⋮ Smooth and rough positive currents ⋮ TWO-SIDED SHIFT SPACES OVER INFINITE ALPHABETS ⋮ Every complex Hénon map is exponentially mixing of all orders and satisfies the CLT ⋮ On Omri Sarig's work on the dynamics on surfaces ⋮ Generalized Hénon mappings and foliation by injective Brody curves ⋮ On Ahlfors currents ⋮ Rigidity theorems for Hénon maps—II ⋮ Pfaff systems, currents and hulls ⋮ Value distribution of derivatives in polynomial dynamics ⋮ Dynamical properties of families of holomorphic mappings ⋮ Pseudoconvex domains with smooth boundary in projective spaces ⋮ Further remarks on rigidity of Hénon maps ⋮ Equidistribution problems in complex dynamics of higher dimension ⋮ Infinite DLR measures and volume-type phase transitions on countable Markov shifts

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