On connecting orbits of semilinear parabolic equations on .
On geometric detection of periodic solutions and chaotic dynamics.
On the existence of homoclinic solutions for almost periodic second order systems
Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...
Orbits connecting singular points in the plane
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.