Equidistribution speed for endomorphisms of projective spaces

被引：24

作者：

Dinh, Tien-Cuong ^{[2
]}

Sibony, Nessim ^{[1
]}

机构：

[1] Univ Paris 11, F-91405 Orsay, France

[2] Univ Paris 06, UMR 7586, Inst Math Jussieu, F-75005 Paris, France

来源：

MATHEMATISCHE ANNALEN | 2010年 / 347卷 / 03期

关键词：

RATIONAL FUNCTIONS; DYNAMICS;

D O I：

10.1007/s00208-009-0445-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a non-invertible holomorphic endomorphism of P(k), f(n) its iterate of order n and mu the equilibrium measure of f. We estimate the speed of convergence in the following known result. If a is a Zariski generic point in P(k), the probability measures, equidistributed on the preimages of a under f(n), converge to mu as n goes to infinity.

引用

页码：613 / 626

页数：14

共 23 条

[1]

[Anonymous], 1995, Ann. of Math. Stud

[2]

[Anonymous], Complex Analytic and Algebraic Geometry

[3]

[Anonymous], ERGOD THEOR DYN SYST

[4]

[Anonymous], 1990, An Introduction to Complex Analysis in Several Variables

[5]

Briend J.-Y., 2001, PUBL MATH-PARIS, V93, P145

[6]

Briend JY, 2009, PUBL MATH-PARIS, P295, DOI 10.1007/s10240-009-0020-0

[7] INVRAIANT SETS UNDER ITERATION OF RATIONAL FUNCTIONS [J].

BROLIN, H .

ARKIV FOR MATEMATIK, 1965, 6 (02) :103-&

[8] On the transfer operator for rational functions on the Riemann sphere [J].

Denker, M ;

Przytycki, F ;

Urbanski, M .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1996, 16 :255-266

[9]

Dinh TC, 2006, COMMENT MATH HELV, V81, P221

[10] Dynamics of polynomial-like mappings [J].

Dinh, TC ;

Sibony, N .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2003, 82 (04) :367-423

← 1 2 3 →