|
Title:
|
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds
|
|
Author:
|
Corbera Subirana, Montserrat; Llibre, Jaume; Teixeira, Marco Antonio
|
|
Other authors:
|
Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals |
|
Notes:
|
In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic
loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere
S2 and a diameter connecting the north with the south pole. The north pole is
an attractor on S2 and a repeller on . The equator of the sphere is a periodic
orbit unstable in the north hemisphere and stable in the south one. The full space
is topologically homeomorphic to the closed ball having as boundary the sphere
S2. We also assume that the flow of X is invariant under a topological straight line
symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient
Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits
of X near L that gives n turns around L in a period. We also exhibit a class of
polynomial vector fields of degree 4 in R3 satisfying this dynamics. |
|
Subject(s):
|
-Matemàtica |
|
Rights:
|
(c) Elsevier
Tots els drets reservats
|
|
Document type:
|
Article
info:eu-repo/acceptedVersion |
|
Published by:
|
Elsevier
|
|
Share:
|
|
