Speaker Alexandre RODRIGUES (University of Porto)
Title. Rank-one strange attractors versus Heteroclinic tangles
In this seminar, we present a mechanism for the emergence of strange attractors (observable chaos) in a two-parametric periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the invariant manifolds of consecutive saddles in the cycle. The first parameter makes the two-dimensional invariant manifolds of consecutive saddles in the cycle to pull apart; the second forces transverse intersection. These relative positions may be determined using the Melnikov method. Generalising , we prove the existence of many complicated dynamical objects in the two-parametric family, ranging from rank-one attractors to Hénon-type strange attractors. We also draw a plausible bifurcation diagram associated to the problem under consideration and we show that the 'occurrence of heteroclinic tangles' is a prevalent phenomenon.
 I. Labouriau, A. Rodrigues, Periodic forcing of a heteroclinic network, Journal of Dynamics and Differential Equations 2021 (to appear), DOI 10.1007/s10884-021-10054-w