The infinitesimal 16th Hilbert problem in dimension zero

被引：9

作者：

Gavrilov, Lubomir

Movasati, Hossein

机构：

[1] Univ Toulouse 3, CNRS, Lab Emile Picard, MIG,UMR 5580, F-31062 Toulouse 9, France

[2] Ochanomizu Univ, Dept Math, Bunkyo Ku, Tokyo 1128610, Japan

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2007年 / 131卷 / 03期

关键词：

Abelian integral; infinitesimal 16th Hilbert problem;

D O I：

10.1016/j.bulsci.2006.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the analogue of the infinitesimal 16th Hilbert problem in dimension zero. Lower and upper bounds for the number of the zeros of the corresponding Abelian integrals (which are algebraic functions) are found. We study the relation between the vanishing of an Abelian integral I(t) defined over Q and its arithmetic properties. Finally, we give necessary and sufficient conditions for an Abelian integral to be identically zero. (c) 2006 Elsevier Masson SAS. All rights reserved.

引用

页码：242 / 257

页数：16

共 50 条

[31] GENERALIZED VAN DER POL EQUATION AND HILBERT'S 16TH PROBLEM
Ioakim, Xenakis
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[32] Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
Dumortier, F
ElMorsalani, M
Rousseau, C
NONLINEARITY, 1996, 9 (05) : 1209 - 1261
[33] Hilbert's 16th problem for quadratic vector fields and cyclicity of graphics
Rousseau, C
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (01) : 437 - 445
[34] Some lower bounds for h(n) in Hilbert's 16th problem
Li J.
Chan H.S.Y.
Chung K.W.
Qualitative Theory of Dynamical Systems, 2002, 3 (2) : 345 - 360
[35] The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems
Barkat, Meriem
Benterki, Rebiha
Llibre, Jaume
NONLINEAR DYNAMICS, 2023, 111 (02) : 1475 - 1484
[36] Symbolic computation of limit cycles associated with Hilbert's 16th problem
Yu, P.
Corless, R.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (12) : 4041 - 4056
[37] Hilbert's 16th problem and bifurcations of planar polynomial vector fields
Li, JB
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (01): : 47 - 106
[38] On Hilbert's 16th Problem for Some Discontinuous Piecewise Differential Systems
Bakhshalizadeh, Ali
Nyamoradi, Nemat
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (11):
[39] The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems
Meriem Barkat
Rebiha Benterki
Jaume Llibre
Nonlinear Dynamics, 2023, 111 : 1475 - 1484
[40] HILBERTS 16TH PROBLEM
WILSON, G
TOPOLOGY, 1978, 17 (01) : 53 - 73

← 1 2 3 4 5 →