(272c) Re-Exploring Noninvertible Systems

Noninvertible maps are defined by functions that can map several points in phase space to a single point. This means that points may not have a single preimage - they may have several, none, or one. Furthermore, because the preimage behavior can change with location in phase space, the interplay between boundaries separating regions of preimage behavior and phase space features can lead to disconnected basins of attraction and segments of invariant curves that fold onto themselves. It this paper, I will re-examine some of the computational work we have done (e.g., [1]) in this area and attempt to assess how the field has evolved since.

[1] Adomaitis, R. A., I. G. Kevrekidis, and R. de la Llave, A computer-assisted study of global dynamic transitions for a noninvertible system, International Journal of Bifurcations and Chaos (2007) 1305-1321.