Rendezvous with Sensitivity

Abstract

Let $(X,d)$ be a compact metric space and $f:X\to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty open subset there are distinct points whose iterates will be $\delta -$apart at same instance. This dynamical property, though being a very weak one, brings in the essence of unpredictability in the system. In this article, we survey various sensitivities and some properties implied by and implying such sensitivities.

arXiv comment10 pages