Homoclinic orbits in degenerate reversible-equivariant systems in R6

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Silva Lima, Mauricio Firmino¹  Teixeira, Marco Antonio² 

[1] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, BR-09210170 Santo Andre, SP, Brazil

[2] Univ Estadual Campinas, Dept Matemat, BR-13083970 Campinas, SP, Brazil

关键词: Equilibrium point;    Periodic orbit;    Homoclinic orbit;    Reversibility;    Normal form;    Resonance;   

DOI  :  10.1016/j.jmaa.2013.02.024

来源: Elsevier

【 摘 要 】

We study the dynamics near an equilibrium point p(0) of a Z(2)xZ(2)-reversible vector field in R-6 with the reversing symmetry or symmetry phi satisfying phi(2) = I and dimFix(phi) = 3. We deal with systems such that X presents at p(0) a degenerate resonance of type 0 : p : q or 0-non-resonant. We are assuming that the linearized system of X (at P-0) has as eigenvalues: lambda(1) = 0 lambda(j) = +/- i alpha(j), j = 2, 3. Our main concern is to find conditions for the existence of families of homoclinic orbits associated to periodic orbits near the equilibrium. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free