✦ LIBER ✦

Dulac Criteria for Autonomous Systems Having an Invariant Affine Manifold

✍ Scribed by Michael Y. Li

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 193 KB
Volume: 199
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0147

No coin nor oath required. For personal study only.

✦ Synopsis

For a class of higher dimensional autonomous systems that have an invariant affine manifold, conditions are derived to preclude the existence of periodic solutions on the invariant manifold. It is established that these conditions are robust under certain types of local perturbations of the vector field. As a consequence, each bounded semitrajectory on the invariant manifold is shown to converge to a single equilibrium using a C 1 closing lemma for this class. Applications to autonomous systems that are homogeneous of degree 1 are also considered.