Title: New methods for fractal and Wada basins
Speaker: Álvar Daza
King Juan Carlos University | Applied Physics
Abstract: In dynamical systems, basins of attraction are defined as the set of initial conditions leading to a particular asymptotic behavior. Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. A special case of fractal boundaries appears when a single boundary separates three or more different basins of attraction. Then we say that the set of basins has the Wada property and initial conditions near that boundary become particularly unpredictable. Although it could seem an odd situation, many physical systems showing this topological property appear in the literature. In this talk, I will review some basic aspects on Wada basins, and then I will describe some new recently developed methods to ascertain the Wada property in dynamical systems. These new methods present important advantages with respect to the previously known method, provide new perspectives on the Wada property and broaden the situations where it can be verified. Also, I will show how the novel concept of basin entropy helps us quantify the unpredictability associated to different basins of attraction and its relation with Wada basins.