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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive

Funktsional. Anal. i Prilozhen., 2024 Volume 58, Issue 4, Pages 3–19 (Mi faa4188)

Multi-dimensional hyperbolic chaos

Sergey Glyzin, Andrei Kolesov

P. G. Demidov Yaroslavl State University, Centre of Integrable Systems, Yaroslavl, Russia

Abstract: We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of $N\geqslant 2$ unidirectionally coupled maps of the two-dimensional torus $\mathbb{T}^2$, each of which is of Arnold's cat map type. We provide sufficient conditions (independent of $N$) under which the chain gives rise to an Anosov diffeomorphism of $\mathbb{T}^{2N}$ for any $N\geqslant 2$.

Keywords: multi-dimensional hyperbolic chaos, Arnold's cat map, Anosov diffeomorphisms, dynamical systems theory.

MSC: 37D20

Received: 11.12.2023
Accepted: 08.04.2024

DOI: 10.4213/faa4188


 English version:
Functional Analysis and Its Applications, 2024, 58:4, 349–361

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© Steklov Math. Inst. of RAS, 2025