SYMMETRIC PERIODIC ORBITS NEAR HETEROCLINIC LOOPS AT INFINITY FOR A CLASS OF POLYNOMIAL VECTOR FIELDS
- 20 November 2006
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos
- Vol. 16 (11), 3401-3410
- https://doi.org/10.1142/s0218127406016884
Abstract
For polynomial vector fields in ℝ3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.Keywords
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