Dulac Criteria for Autonomous Systems
نویسندگان
چکیده
For a class of hhgher dimensional autonomous systems that have an invariant aane 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 type of local perturbations of the vector eld. As a consequence, each bounded semitrajectory on the invariant manifold is shown to converge to an single equilibrium using a C 1 closing lemma for this class. Applications to autonomous systems that are homogeneous of degree 1 are also considered.
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