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arXiv · 2402.15479

Dynamical systems of an infinite-dimensional non-linear operator

U. R. Olimov·U. A. Rozikov
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Abstract

We investigate discrete-time dynamical systems generated by an infinite-dimensional non-linear operator that maps the Banach space $l_1$ to itself. It is demonstrated that this operator possesses up to seven fixed points. By leveraging the specific form of our operator, we illustrate that analyzing the operator can be simplified to a two-dimensional approach. Subsequently, we provide a detailed description of all fixed points, invariant sets for the two-dimensional operator and determine the set of limit points for its trajectories. These results are then applied to find the set of limit points for trajectories generated by the infinite-dimensional operator.

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U. R. Olimov, U. A. Rozikov. 2024-02-23. Dynamical systems of an infinite-dimensional non-linear operator. https://arxiv.org/abs/2402.15479

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