The Topological Sensitivity with respect to Furstenberg Families

Abstract

In this work, a dynamical system X,f means that X is a topological space and f:X⟶X is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, n-topological sensitivity, and multisensitivity and present some of their basic features and sufficient conditions for a dynamical system to possess some sensitivities. Actually, it is proved that every topologically ergodic but nonminimal system is syndetically sensitive and a weakly mixing system is n-thickly topologically sensitive and multisensitive under the assumption that X admits some separability.