Constancy of discrete Lyapunov functionals on stable/linearly stable minimal sets and its applications

Yan, Kaige; Zhou, Dun

doi:10.1090/proc/16703

Constancy of discrete Lyapunov functionals on stable/linearly stable minimal sets and its applications
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by Kaige Yan and Dun Zhou;

Proc. Amer. Math. Soc. 153 (2025), 2419-2432

DOI: https://doi.org/10.1090/proc/16703

Published electronically: April 3, 2025

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Abstract:

We consider the skew-product semiflow for non-autonomous system with discrete Lyapunov functional, and prove the residually constancy of discrete Lyapunov functional on any stable or linearly stable (in strongly monotone systems) minimal set. As an application, we prove that any stable or linearly stable minimal set of time almost-periodic monotone cyclic feedback system can be residually embedded into a two-dimensional plane. Besides, the results can also be used to some non-autonomous delay equations.

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Proceedings of the American Mathematical Society

Constancy of discrete Lyapunov functionals on stable/linearly stable minimal sets and its applications
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Abstract: