Rendezvous with sensitivity. Issue 8 (2nd August 2020) - Nagar, Anima
Abstract : Let ( X, d ) be a compact metric space and f : X → 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 δ such that in each non-empty open subset there are distinct points whose iterates will be δ -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.