Periodic points for area-preserving birational maps of surfaces

被引：10

作者：

Iwasaki, Katsunori ^{[1
]}

Uehara, Takato ^{[1
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Higashi Ku, Fukuoka 8128581, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2010年 / 266卷 / 02期

关键词：

ELLIPTIC COMPLEXES; HOLOMORPHIC MAPS; FORMULA; CURVES; DYNAMICS; INDEXES;

D O I：

10.1007/s00209-009-0570-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is a basic problem to count the number of periodic points of a surface mapping, since the growth rate of this number as the period tends to infinity is an important dynamical invariant. However, this problem becomes difficult when the map admits curves of periodic points. In this situation we give a precise estimate of the number of isolated periodic points for an area-preserving birational map of a projective complex surface.

引用

页码：289 / 318

页数：30

共 50 条

[31] Least Number of Periodic Points of Self-maps of Lie Groups
Jezierski, Jerzy
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (09) : 1477 - 1494
[32] Area-preserving curvature flow of one-dimensional graphs and application to smoothing of dynamic PET data
Baker, Charles
MATHEMATISCHE NACHRICHTEN, 2015, 288 (14-15) : 1592 - 1601
[33] Periodic points and arithmetic degrees of certain rational self-maps
Wang, Long
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2024, 76 (03) : 713 - 738
[34] Periodic points, linearizing maps, and the dynamical Mordell-Lang problem
Ghioca, D.
Tucker, T. J.
JOURNAL OF NUMBER THEORY, 2009, 129 (06) : 1392 - 1403
[35] Pseudo-periodic Maps and Degeneration of Riemann Surfaces Preface
Matsumoto, Yukio
Maria Montesinos-Amilibia, Jose
PSEUDO-PERIODIC MAPS AND DEGENERATION OF RIEMANN SURFACES, 2011, 2030 : VII - +
[36] Nonwandering set of points of skew-product maps with base having closed set of periodic points
Garcia Guirao, Juan Luis
Garcia Rubio, Raquel
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 362 (02) : 350 - 354
[37] Lagrangian descriptors for two dimensional, area preserving, autonomous and nonautonomous maps
Lopesino, Carlos
Balibrea, Francisco
Wiggins, Stephen
Mancho, Ana M.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 27 (1-3) : 40 - 51
[38] Super-potentials, densities of currents and number of periodic points for holomorphic maps
Tien-Cuong Dinh
Viet-Anh Nguyen
Duc-Viet Vu
ADVANCES IN MATHEMATICS, 2018, 331 : 874 - 907
[39] PRESENTATIONS OF PERIODIC MAPS ON ORIENTED CLOSED SURFACES OF GENERA UP TO 4
Hirose, Susumu
OSAKA JOURNAL OF MATHEMATICS, 2010, 47 (02) : 385 - 421
[40] Minimal number of periodic points for smooth self-maps of S3
Graff, Grzegorz
Jezierski, Jerzy
FUNDAMENTA MATHEMATICAE, 2009, 204 (02) : 127 - 144

← 1 2 3 4 5 →