We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problemdependent critical value so-called event collisions occur. This paper classifies and analyzes event collisions, a special type of discontinuity induced bifurcations, for periodic orbits. Our focus isâ€¦ (More)

Time-delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current output and the output from a fixed time T ago. Thus, any periodic orbit of period T in the feedback-controlled system isâ€¦ (More)

Introduction. In his monograph [l], CsÃ¡szÃ¡r introduced the notion of a syntopogenous space, which generalized the notions of a topological space, a proximity space, and a uniform space. Although CsÃ¡szÃ¡r was able to obtain many of the usual theorems of general topology in this more general setting, the basic topological notion of connectedness was notâ€¦ (More)