TRANSVERSAL PERIODIC-TO-PERIODIC HOMOCLINIC ORBITS IN SINGULARLY PERTURBED SYSTEMS

被引：0

作者：

Battelli, Flaviano ^{[1
]}

Palmer, Ken ^{[2
]}

机构：

[1] Univ Ancona, Fac Ingn, Dipartimento Sci Matemat, I-60100 Ancona, Italy

[2] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2010年 / 14卷 / 02期

关键词：

Singular perturbation; homoclinic bifurcation; invariant manifolds; Melnikov function; Sil'nikov orbits; CONNECTIONS; MANIFOLDS; POINTS;

D O I：

10.3934/dcdsb.2010.14.367

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a singularly perturbed system with a normally hyperbolic centre manifold. Assuming the existence of a fast homoclinic orbit to a point of the centre manifold belonging to a hyperbolic periodic solution for the slow system, we prove an old and a new result concerning the existence of solutions of the singularly perturbed system that are homoclinic to a periodic solution of the system on the centre manifold. We also give examples in dimensions greater than three of Sil'nikov [16] periodic-to-periodic homoclinic orbits.

引用

页码：367 / 387

页数：21

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