On the number of limit cycles bifurcating from a non-global degenerated center

被引:9
作者
Gasull, Armengol [1 ]
Li, Chengzhi
Liu, Changjian
机构
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Bellaterra, Barcelona, Spain
[2] Peking Univ, LMAM, Beijing 100871, Peoples R China
[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
关键词
Abelian integral; limit cycle; planar vector field; degenerated center;
D O I
10.1016/j.jmaa.2006.06.047
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) dH = 0, where H is the quasi-homogeneous Hamiltonian H(x, y) = x(2k)/(2k) + y(2)/2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码:268 / 280
页数:13
相关论文
共 21 条
[1]  
Basarab-Horwath P., 1988, NIEUW ARCH WISK, V6, P295
[2]  
Broer H., 1991, STRUCTURES DYNAMICS
[3]   POLYNOMIAL SYSTEMS - A LOWER-BOUND FOR THE HILBERT-NUMBERS [J].
CHRISTOPHER, CJ ;
LLOYD, NG .
PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1995, 450 (1938) :219-224
[4]  
Coll B, 2005, DYNAM CONT DIS SER A, V12, P275
[5]   A relation between small amplitude and big limit cycles [J].
Gasull, A ;
Torregrosa, J .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2001, 31 (04) :1277-1303
[6]   On the nonexistence, existence and uniqueness of limit cycles [J].
Giacomini, H ;
Llibre, J ;
Viano, M .
NONLINEARITY, 1996, 9 (02) :501-516
[7]  
Hilbert D, 1901, ARCH MATH PHYS, V1, P213
[8]  
Itenberg I, 2000, DUKE MATH J, V102, P1
[9]  
JU S, 1969, MAT SBORNIK, V78, P360
[10]  
Li J., 2003, QUAL THEORY DYN SYST, V3, P345, DOI DOI 10.1007/BF02969411