Geodesic
Dynamical Systems of an Infinite-Dimensional Nonlinear Operator on the Banach Space $l_1$
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 4, pp. 685-703

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We investigate discrete-time dynamical systems generated by an infinite-dimensional nonlinear 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.
Keywords: infinite-dimensional operator, trajectory, fixed point, limit point, partial order 
@article{ND_2024_20_4_a14,
     author = {U. R. Olimov and U. A. Rozikov},
     title = {Dynamical {Systems} of an {Infinite-Dimensional} {Nonlinear} {Operator} on the {Banach} {Space} $l_1$},
     journal = {Russian journal of nonlinear dynamics},
     pages = {685--703},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2024_20_4_a14/}
}
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U. R. Olimov; U. A. Rozikov. Dynamical Systems of an Infinite-Dimensional Nonlinear Operator on the Banach Space $l_1$. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 4, pp. 685-703. http://geodesic.mathdoc.fr/item/ND_2024_20_4_a14/