Entropy properties of rational endomorphisms of the Riemann sphere
TLDR
In this article, the existence of a unique measure of maximal entropy for rational endomorphisms of the Riemann sphere is established and the equidistribution of pre-images and periodic points with respect to this measure is proved.Abstract:
In this paper the existence of a unique measure of maximal entropy for rational endomorphisms of the Riemann sphere is established. The equidistribution of pre-images and periodic points with respect to this measure is proved.read more
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Complex dynamics in higher dimensions
John Erik Fornæss,Nessim Sibony +1 more
TL;DR: The field of complex dynamics in higher dimensions was initiated in the 1920s by Fa-tou as discussed by the authors, who was motivated by studies in Newton's method, celestial mechanics and functional equations.
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Potential Theory and Dynamics on the Berkovich Projective Line
Matthew Baker,Robert Rumely +1 more
TL;DR: In this article, the authors develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field.
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Conformal Fractals: Ergodic Theory Methods
TL;DR: In this article, the authors define a metric space with invariant probability measures of positive Lyapunov exponent and a set of conformal expanding repellers in the Riemann sphere.
Journal ArticleDOI
Polynomial diffeomorphisms of C2. IV: The measure of maximal entropy and laminar currents.
TL;DR: In this paper, the algebraic degree of the polynomial is defined as the maximum of the degrees of the coordinate functions of the holomorphic polynomials of the system.
References
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BookDOI
Equilibrium states and the ergodic theory of Anosov diffeomorphisms
TL;DR: Gibbs Measures and Gibbs measures have been used in this article to define Axiom a Diffeomorphisms for general Thermodynamic Formalism and Ergodic Theory of Axiom-a-Diffeomorphism.
Journal ArticleDOI
Sur les équations fonctionnelles
TL;DR: The Bulletin de la S. M. F. as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).
Journal ArticleDOI
Topological entropy for noncompact sets
Journal ArticleDOI
Statistical mechanics of a one-dimensional lattice gas
TL;DR: In this article, the statistical mechanics of an infinite one-dimensional classical lattice gas were studied and it was shown that for a large class of interactions, such a system has no phase transition and the equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations.