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Indexed by:期刊论文

Date of Publication:2018-05-30

Journal:MODERN PHYSICS LETTERS B

Included Journals:SCIE

Volume:32

Issue:15

ISSN No.:0217-9849

Key Words:Sensitivity; multi-sensitivity; multi-transitivity; dynamical system

Abstract:Consider the surjective continuous map f: X -> X defined on a compact metric space X. Let K(X) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric and define (f) over bar: K(X) -> K(X) by (f) over bar (A) = {f(a), a is an element of A} for any A is an element of K(X). In this paper, we introduce several stronger versions of sensitivities, such as multi sensitivity with respect to a vector, N-sensitivity, strong multi-sensitivity. We obtain some basic properties of the concepts of these sensitivities and discuss the relationships with other sensitivities for continuous self-map on [0, 1]. Some sufficient conditions for a dynamical system to be N-sensitive are presented. Also, it is shown that the strong multi-sensitivity off implies that (f) over bar is N-sensitive. In turn, the N-sensitivity of (f) over bar implies that f is N-sensitive. In particular, it is proved that if f is a multi-transitive map with dense periodic sets, then f is N-sensitive. Finally, we give a multi-sensitive example which is not N-sensitive.