Work

Dynamical systems of an infinite-dimensional non-linear operator

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.15479

Authors: Olimov, U. R., Rozikov, U. A.

Institutions: Academy of Sciences Republic of Uzbekistan, National University of Uzbekistan

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Innovative Development of the Republic of Uzbekistan, Centers for Disease Control and Prevention

Award: G1870190849

OpenAlex ID: W4392182827

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