Conditions are given that guarantee the nonexistence of periodic orbits lying entirely in a simply connected set. The conditions are formulated in terms of matrix inequalities involving the variational equation. For systems defined in R2 the conditions are equivalent to Bendixon’s criterion. A connection with analytic estimates of the Hausdorff dimension of invariant compact sets is emphasized.
|Title of host publication||15th Triennial World Congress of the International Federation of Automatic Control|
|Place of Publication||Spain, Barcelona|
|Publication status||Published - 2002|