Dynamical behavior of a general non-autonomous dynamical system
Submitted: 2024-04-03
|Accepted: 2025-01-10
|Published: 2025-04-01
Copyright (c) 2025 Sushmita Yadav, Puneet Sharma
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
non-autonomous dynamical systems, equicontinuity, minimal systems, almost periodicity, proximality
Supporting agencies:
MoE
National Board for Higher Mathematics (NBHM)
Abstract:
In this work, we investigate dynamical notions such as minimality, almost periodicity, equicontinuity, transitivity, proximality and periodicity for a general non-autonomous dynamical system. We provide necessary and sufficient conditions for a non-autonomous system to be minimal. We prove that for an equicontinuous system (X,F), if x is almost periodic then OH(x) is uniformly almost periodic. We also establish preservance of almost periodicity under uniform convergence. We also establish some results capturing the qualitative behavior of a general non-autonomous dynamical system.
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