Saddle connections in planar systems

Hana Lichardova

Address. Dept. of Math., Faculty of Electrical Engineering and Information Technology SUT, Ilkovicova 3, 812 19 Bratislava,                Slovakia

E-mail: lichardova@kmat.elf.stuba.sk

Abstract. The class of planar autonomous systems with a small parameter-dependent perturbation is considered. We derive a sufficient condition for existence of a saddle connection in such system.

AMSclassification. 34C37

Keywords. Saddle connection, stable and unstable manifolds, small perturbation, Hamiltonian system