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Equilibrium states of endomorphisms of [formula omitted] I: Existence and properties.
- Source :
-
Journal de Mathematiques Pures et Appliquees . Apr2023, Vol. 172, p164-201. 38p. - Publication Year :
- 2023
-
Abstract
- We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on P k = P k (C) by a holomorphic endomorphism and a suitable continuous weight. This method allows us to prove the existence and uniqueness of the equilibrium state and conformal measure for very general weights (due to Denker-Przytycki-Urbański in dimension 1 and Urbański-Zdunik in higher dimensions, both in the case of Hölder continuous weights). We establish a number of properties of the equilibrium states, including mixing, K-mixing, mixing of all orders, and an equidistribution of repelling periodic points. Our analytic method replaces all distortion estimates on inverse branches with a unique, global, estimate on dynamical currents, and allows us to reduce the dynamical questions to comparisons between currents and their potentials. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HOLDER spaces
*ENDOMORPHISMS
*EQUILIBRIUM
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 172
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 162502647
- Full Text :
- https://doi.org/10.1016/j.matpur.2023.01.007