Rendezvous with sensitivity. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: Nagar, Anima
• Is Part Of: Journal of difference equations and applications. Volume 26:Issue 8(2020)
• Page Start: 1048
• Page End: 1058
• Publication Date: 2020-08-02
• Subjects: Minimality -- sensitivity -- equicontinuity -- Auslander–Yorke dichotomy -- chaos; 37B05 -- 54H20; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2019.1678598
• Languages: English
• ISSNs: 1023-6198

Abstract

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.