Výsledky vyhledávání - "Gabriel Vigny"

Approximation of non-archimedean Lyapunov exponents and applications over global fields

Autor: Gabriel Vigny, Yûsuke Okuyama, Thomas Gauthier

Publikováno v: Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (12), pp.8963-9011. ⟨10.1090/tran/8232⟩

Let $K$ be an algebraically closed field of characteristic 0 that is complete with respect to a non-archimedean absolute value. We establish a locally uniform approximation formula of the Lyapunov exponent of a rational map $f$ of $\mathbb{P}^1$ of d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8269ef35184dc715cbfe919c2b540b51
https://hal.archives-ouvertes.fr/hal-03510161

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Value distribution of derivatives in polynomial dynamics

Autor: Yûsuke Okuyama, Gabriel Vigny

Publikováno v: Ergodic Theory and Dynamical Systems
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2021, 41 (12), pp.3780-3806. ⟨10.1017/etds.2020.125⟩

For every $m\in \mathbb {N}$ , we establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any given value in $\mathbb {C}\setminus \{0\}$ under the $m$ th order derivatives of the iterates of a polynomials $f\in

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http://arxiv.org/abs/1904.06858

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Collet, Eckmann and the bifurcation measure

Autor: Matthieu Astorg, Thomas Gauthier, Gabriel Vigny, Nicolae Mihalache

Publikováno v: Inventiones Mathematicae
Inventiones Mathematicae, Springer Verlag, 2019, 217 (3), pp.749-797. ⟨10.1007/s00222-019-00874-5⟩

The moduli space $$\mathcal {M}_d$$ of degree $$d\ge 2$$ rational maps can naturally be endowed with a measure $$\mu _{\text{ bif }}$$ detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measur

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9cbf3144f8c27fd7dfc7c15d07cdcbac
https://hal.archives-ouvertes.fr/hal-01888305

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The bifurcation measure has maximal entropy

Autor: Thomas Gauthier, Gabriel Vigny, Henry de Thelin

Publikováno v: Israël Journal of Mathematics
Israël Journal of Mathematics, Hebrew University Magnes Press, 2020, 235 (1), pp.213-243. ⟨10.1007/s11856-019-1955-6⟩

Let $\Lambda$ be a complex manifold and let $(f_\lambda)_{\lambda\in \Lambda}$ be a holomorphic family of rational maps of degree $d\geq 2$ of $\mathbb{P}^1$. We define a natural notion of entropy of bifurcation, mimicking the classical definition of

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Entropy of meromorphic maps acting on analytic sets

Autor: Gabriel Vigny, Henry de Thelin

Publikováno v: Indiana University Mathematics Journal
Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2021, 70 (1), pp.157-178. ⟨10.1512/iumj.2021.70.8290⟩

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l \leq k$. Fo

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Hyperbolic components of rational maps: Quantitative equidistribution and counting

Autor: Gabriel Vigny, Yûsuke Okuyama, Thomas Gauthier

Publikováno v: Commentarii Mathematici Helvetici
Commentarii Mathematici Helvetici, European Mathematical Society, 2019, 94 (2), pp.347-398. ⟨10.4171/CMH/462⟩

Let $\Lambda$ be a quasi-projective variety and assume that, either $\Lambda$ is a subvariety of the moduli space $\mathcal{M}_d$ of degree $d$ rational maps, or $\Lambda$ parametrizes an algebraic family $(f_\lambda)_{\lambda\in\Lambda}$ of degree $

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http://arxiv.org/abs/1705.05276

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Exponential decay of correlations for generic regular birational maps of $$\mathbb {P}^k$$ P k

Autor: Gabriel Vigny

Publikováno v: Mathematische Annalen
Mathematische Annalen, Springer Verlag, 2015, 362 (3-4), pp.1033-1054. ⟨10.1007/s00208-014-1131-6⟩

We prove the exponential decay of correlations for $C^\alpha $-observables (\(0

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::682cd248c286a69039b9e88973cb7be4
https://doi.org/10.1007/s00208-014-1131-6

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Hyperbolic measure of maximal entropy for generic rational maps of \mathbb{P}^k

Autor: Gabriel Vigny

Publikováno v: Annales de l’institut Fourier. 64:645-680

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https://doi.org/10.5802/aif.2861

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DISTRIBUTION OF POSTCRITICALLY FINITE POLYNOMIALS III: COMBINATORIAL CONTINUITY

Autor: Thomas Gauthier, Gabriel Vigny

Publikováno v: Fundamenta Mathematicae
Fundamenta Mathematicae, Instytut Matematyczny, Polskiej Akademii Nauk, 2019, 244 (1), pp.17-48. ⟨10.4064/fm220-2-2018⟩

In the first part of the present paper, we continue our study of distribution of postcritically finite parameters in the moduli space of polynomials: we show the equidistribution of Misiurewicz parameters with prescribed combinatorics toward the bifu

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https://hal.archives-ouvertes.fr/hal-01265616/file/DistribPCF.pdf

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Lelong-Skoda Transform for Compact Kähler Manifolds and Self-Intersection Inequalities

Autor: Gabriel Vigny

Publikováno v: The Journal of Geometric Analysis
The Journal of Geometric Analysis, Springer, 2009, 19 (2), pp.433-451. ⟨10.1007/s12220-008-9056-5⟩

Let X be a compact Kahler manifold of dimension k and T be a positive closed current on X of bidimension (p,p) (1≤p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1184e5f08cd1e4207aba368665f73a56
https://doi.org/10.1007/s12220-008-9056-5

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