Homoclinic phenomena in conservative dynamical systems
Marina Gonchenko (Universitat de Barcelona)
Meeting ID: 923 3793 7169
We study homoclinic orbits in conservative dynamical systems. Such orbits, called homoclinic by Poincaré, are of great interest in the theory of dynamical systems since their presence implies chaotic dynamics. We study area-preserving maps (APMs) with a nontransversal homoclinic orbit (homoclinic tangency) to a saddle fixed point and we prove the existence of cascades of elliptic periodic points near the given homoclinic trajectory. We also study the phenomenon of the coexistence of infinitely many periodic orbits of different large periods (called global resonance). We consider the related problems in different types of APMs (symplectic maps and non-orientable APMs) with quadratic or cubic tangencies.