2026-04-17T08:15:01Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1938462025-12-05T09:53:41Zcom_2072_1057col_2072_478917col_2072_478920

00925njm 22002777a 4500 dc Gonchenko, Sergey V. author Simó, Carles author Vieiro Yanes, Arturo author 2023-02-20T18:34:06Z 2023-02-20T18:34:06Z 2013-01-17 2023-02-20T18:34:07Z We consider 2D flows with a homoclinic figure-eight to a dissipative saddle. We study the rich dynamics that such a system exhibits under a periodic forcing. First, we derive the bifurcation diagram using topological techniques. In particular, there is a homoclinic zone in the parameter space with a non-smooth boundary. We provide a complete explanation of this phenomenon relating it to primary quadratic homoclinic tangency curves which end up at some cubic tangency (cusp) points. We also describe the possible attractors that exist (and may coexist) in the system. A main goal of this work is to show how the previous qualitative description can be complemented with quantitative global information. To this end, we introduce a return map model which can be seen as the simplest one which is 'universal' in some sense. We carry out several numerical experiments on the model, to check that all the objects predicted to exist by the theory are found in the model, and also to investigate new properties of the system. Teoria de la bifurcació Teoria ergòdica Sistemes dinàmics de baixa dimensió Òrbites Bifurcation theory Ergodic theory Low-dimensional dynamical systems Orbits Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight