Equilibrium measures for holomorphic endomorphisms of complex projective spaces

DOI10.4064/fm220-1-3zbMath1276.37026OpenAlexW2013248052MaRDI QIDQ4900173

Anna Zdunik, Mariusz Urbański

Publication date: 14 January 2013

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/fm220-1-3

zbMATH Keywords

Perron-Frobenius operatorJulia setcomplex projective spacetopological pressureholomorphic dynamicsequilibrium stateHölder continuous potential

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) 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) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

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Higher bifurcations for polynomial skew products ⋮ Fine inducing and equilibrium measures for rational functions of the Riemann sphere ⋮ Large entropy measures for endomorphisms of \(\mathbb{CP}^k\) ⋮ Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022 ⋮ Equilibrium states of endomorphisms of \(\mathbb{P}^k\). I: Existence and properties ⋮ Low-temperature phase transitions in the quadratic family ⋮ Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces ⋮ Measures and dynamics on Noetherian spaces ⋮ Thin annuli property and exponential distribution of return times for weakly Markov systems

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