Equidistribution speed for endomorphisms of projective spaces

Dinh, Tien-Cuong; Sibony, Nessim

doi:10.1007/s00208-009-0445-2

Cited by 33 publications

(28 citation statements)

References 25 publications

(53 reference statements)

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“…functions (see Theorem 3.2) which are used as test functions for measures and also some analysis of the critical set in order to localize the exceptional set E . We refer the reader to [33] for more precise statements and history of the problem. The similar statement with the same proof holds for algebraically expanding holomorphic maps on compact Kähler manifolds.…”

Section: Equidistribution Of Orbits Of Points and Varietiesmentioning

confidence: 99%

Equidistribution problems in complex dynamics of higher dimension

Dinh

Sibony

2017

Int. J. Math.

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ABSTRACT. Equidistribution of the orbits of points, subvarieties or of periodic points in complex dynamics is a fundamental problem. It is often related to strong ergodic properties of the dynamical system and to a deep understanding of analytic cycles, or more generally positive closed currents, of arbitrary dimension and degree. The later topic includes the study of the potentials and super-potentials of positive closed currents, their intersection with or without dimension excess. In this paper, we will survey some results and tools developed during the last two decades. Related concepts, new techniques and open problems will be presented.Classification AMS 2010: 32H, 32U, 37F.

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Section: Equidistribution Of Orbits Of Points and Varietiesmentioning

confidence: 99%

Equidistribution problems in complex dynamics of higher dimension

Dinh

Sibony

2017

Int. J. Math.

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“…From the dynamics point of view, as seen in Dinh-Sibony [5, Theorem 1.3, Corollary 1.4], f : P n → P n behaves nicely exactly outside those f −1 -stabilized subvarieties. We refer to Fornaess-Sibony [7], and [5] for further references.…”

Section: 4mentioning

confidence: 99%

Invariant hypersurfaces of endomorphisms of the projective 3-space

Zhang¹

2013

Affine Algebraic Geometry

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“…Using the analytic tools given by the work of Drasin and Okuyama [10], or Dinh and Sibony [9], we get the following:…”

Section: Forewordmentioning

confidence: 99%

Computability of Brolin-Lyubich Measure

Binder

Braverman

Rojas

et al. 2011

Commun. Math. Phys.

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Brolin-Lyubich measure $\lambda_R$ of a rational endomorphism $R:\riem\to\riem$ with $\deg R\geq 2$ is the unique invariant measure of maximal entropy $h_{\lambda_R}=h_{\text{top}}(R)=\log d$. Its support is the Julia set $J(R)$. We demonstrate that $\lambda_R$ is always computable by an algorithm which has access to coefficients of $R$, even when $J(R)$ is not computable. In the case when $R$ is a polynomial, Brolin-Lyubich measure coincides with the harmonic measure of the basin of infinity. We find a sufficient condition for computability of the harmonic measure of a domain, which holds for the basin of infinity of a polynomial mapping, and show that computability may fail for a general domain

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Equidistribution speed for endomorphisms of projective spaces

Cited by 33 publications

References 25 publications

Equidistribution problems in complex dynamics of higher dimension

Equidistribution problems in complex dynamics of higher dimension

Invariant hypersurfaces of endomorphisms of the projective 3-space

Computability of Brolin-Lyubich Measure

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