Stronger Forms of Transitivity and Sensitivity for Nonautonomous Discrete Dynamical Systems and Furstenberg Families View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-06

AUTHORS

Risong Li, Yu Zhao, Hongqing Wang, Haihua Liang

ABSTRACT

Let (Y, d) be a nontrivial metric space and (Y, g1,∞) be a nonautonomous discrete dynamical system given by sequences (gl)l=1∞ of continuous maps gl : Y → Y and let F, F1 and F2 be given shift-invariant Furstenberg families. In this paper, we study stronger forms of transitivity and sensitivity for nonautonomous discrete dynamical systems by using Furstenberg family. In particular, we discuss the F-transitivity, F-mixing, F-sensitivity, F-collective sensitivity, F-synchronous sensitivity, (F1,F2)-sensitivity and F-multi-sensitivity for the system (Y, g1,∞) and show that under the conditions that gj is semi-open and satisfies gj ∘ g = g ∘ gj for each j ∈ {1, 2, ⋯ } and that ∑j=1∞D(gj,g)exists (i.e., ∑j=1∞D(gj,g)<+∞), the following hold: (Y, g1,∞) is F-transitive if and only if so is (Y, g).(Y, g1,∞) is F-mixing if and only if so is (Y, g).(Y, g1,∞) is F-sensitive if and only if so is (Y, g).(Y, g1,∞) is (F1,F2)-sensitive if and only if so is (Y, g).(Y, g1,∞) is F-collectively sensitive if and only if so is (Y, g).(Y, g1,∞) is F-synchronous sensitive if and only if so is (Y, g).(Y, g1,∞) is F-multi-sensitive if and only if so is (Y, g). (Y, g1,∞) is F-transitive if and only if so is (Y, g). (Y, g1,∞) is F-mixing if and only if so is (Y, g). (Y, g1,∞) is F-sensitive if and only if so is (Y, g). (Y, g1,∞) is (F1,F2)-sensitive if and only if so is (Y, g). (Y, g1,∞) is F-collectively sensitive if and only if so is (Y, g). (Y, g1,∞) is F-synchronous sensitive if and only if so is (Y, g). (Y, g1,∞) is F-multi-sensitive if and only if so is (Y, g). The above results extend the existing ones. More... »

PAGES

1-18

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10883-019-09437-6

DOI

http://dx.doi.org/10.1007/s10883-019-09437-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112540808


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