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On a paradoxical property of the shifting mapping on an infinite-dimensional tori
- Authors: Glyzin S.D.1, Kolesov A.Y.1
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Affiliations:
- Center of Integrable Systems, P.G. Demidov Yaroslavl State University
- Issue: Vol 515, No 1 (2024)
- Pages: 28-33
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/259874
- DOI: https://doi.org/10.31857/S2686954324010041
- EDN: https://elibrary.ru/ZTWIWM
- ID: 259874
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Abstract
An infinite-dimensional torus T∞=lp/2πZ∞, where lp, p ≥ 1 – space of sequences, Z∞ – natural integer lattice in lp, is considered. We study the classical question in the theory of dynamical systems about the behavior of trajectories of a shift mapping on the specified torus. More precisely, some sufficient conditions are proposed that guarantee the emptiness of the ω-limit and α-limit sets of any of the shift mapping onto T∞.
About the authors
S. D. Glyzin
Center of Integrable Systems, P.G. Demidov Yaroslavl State University
Author for correspondence.
Email: glyzin.s@gmail.com
Russian Federation, Yaroslavl
A. Yu. Kolesov
Center of Integrable Systems, P.G. Demidov Yaroslavl State University
Email: andkolesov@mail.ru
Russian Federation, Yaroslavl
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