Families of periodic orbits in resonant reversible systems

被引：0
作者：
Maurício Firmino Silva Lima
Marco Antonio Teixeira
机构：
[1] Universidade Federal do ABC,CMCC
[2] Universidade Estadual de Campinas,Departamento de Matemática
来源：
Bulletin of the Brazilian Mathematical Society, New Series | 2009年 / 40卷
关键词：
equilibrium point; periodic orbit; reversibility; normal form; resonance; 34C25; 37C25; 37C14;
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摘要：
We study the dynamics near an equilibrium point p0 of a Z2(ℝ)-reversible vector field in ℝ2n with reversing symmetry R satisfying R2 = I and dimFix(R) = n. We deal with one-parameter families of such systems Xλ such that X0 presents at p0 a degenerate resonance of type 0: p: q. We are assuming that the linearized system of X0 (at p0) has as eigenvalues: λ1 = 0 and λj = ±iαj, j = 2, … n. Our main concern is to find conditions for the existence of one-parameter families of periodic orbits near the equilibrium.
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页码：511 / 537
页数：26
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