Large entropy measures and their supports
В данной статье приведено новое доказательство теоремы de Th´ elin и Dinh о том, что бассейн
мер с большой энтропией для эндоморфизмов лежит в множестве Жюлиа. Доказательство
основано на скорости сходимости к равномерно распределённой мере.
1. Sardor Bazarbaev, Fabrizio Bianchi and Karim Rakhimov, On the support of measures of large entropy
for polynomial-like maps. Anal.Math.Phys. 15, 69 (2025).
2. Jean-Yves Briend and Julien Duval, Deux caract´ erisations de la mesure d’´ equilibre d’un endomorphisme
de P k (C), Publications math´ ematiques de l’IH ´ ES, 93 (2001), 145-159.
3. Fabrizio Bianchi and Tien-Cuong Dinh, Equilibrium states of endomorphisms of P k I: existence and
properties, Journal de math´ ematiques pures et appliqu´ ees 172 (2023), 164-201.
4. Fabrizio Bianchi and Tien-Cuong Dinh, Equilibrium states of endomorphisms of P k : spectral gap and limit
theorems, Geometric And Functional Analysis (GAFA) 34 (2024), 1006-1051.
5. Christophe Dupont, Large entropy measures for endomorphisms of CP k , Israel Journal of Mathematics
192 (2012), 505-533.
6. Tien-Cuong Dinh and Nessim Sibony, Equidistribution speed for endomorphisms of projective spaces.
Mathematische Annalen 347 (2010), 613-626.
7. Tien-Cuong Dinh and Nessim Sibony, Dynamics in several complex variables: endomorphisms of projective
spaces and polynomial-like mappings, in Holomorphic dynamical systems, Eds. G. Gentili, J. Guenot, G.
Patrizio, Lect. Notes in Math. 1998 (2010), Springer, Berlin, 165-294.
8. Henry de Th´ elin, Sur la construction de mesures selles, Annales de l’institut Fourier 56 (2006), no. 2,
337-372.
9. Tien-Cuong Dinh, Attracting current and equilibrium measure for attractors on P k , Journal of Geometric
Analysis 17 (2007), 227-244.
10. Mikhael Gromov, On the entropy of holomorphic maps, L’Enseignement Math´ ematique 49 (2003) no. 3-4,
217-235.
11. Kenneth Falconer, Fractal geometry (book). Mathematical Foundations and Applications. Second Edition.
12. Nessim Sibony, Dynamique des applications rationnelles de P k , Panoramas et Synth` eses, 8 (1999), 97-185.
13. Micha l Szostakiewicz, Mariusz UrbaЕ„ski, and Anna Zdunik, Stochastics and thermodynamics for
equilibrium measures of holomorphic endomorphisms on complex projective spaces, Monatshefte für
Mathematik 174 (2014), no. 1, 141-162.
14. Mariusz UrbaЕ„ski and Anna Zdunik, Equilibrium measures for holomorphic endomorphisms of complex
projective spaces, Fundamenta Mathematicae 220 (2013) 23-69.
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