Dynamics Of Finitely Generated Non-Autonomous Systems

2018/10/02 by Manish Raghav, Puneet Sharma, Raghav, Manish +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Chaos control and synchronization

paper · pdf · doi:10.48550/arxiv.1810.01167

Abstract

In this paper, we discuss dynamical behavior of a non-autonomous system generated by a finite family \mathbbF. In the process, we relate the dynamical behavior of the non-autonomous system generated by the family \mathbbF=\f₁,f₂,…,f_k\ with the dynamical behavior of the system (X,f_k∘ f_k-1∘…∘ f₁). We discuss properties like minimality, equicontinuity, proximality and various forms of sensitivities for the two systems. We derive conditions under which the dynamical behavior of (X,f_k∘ f_k-1∘…∘ f₁) is carried forward to (X,\mathbbF) (and vice-versa). We also give examples to illustrate the necessity of the conditions imposed.

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