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arXiv · 2305.05929

Analogues of Jacobi and Weyl Theorems for Infinite-Dimensional Tori

V. Zh. Sakbaev·I. V. Volovich
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Abstract

Generalizations of the Jacobi and Weyl theorems on finite-dimensional linear flows to the case of linear flows on infinite-dimensional tori are presented. Conditions for periodicity, non-wandering, ergodicity and transitivity of trajectories of an infinite-dimensional linear flow are obtained. It is shown that for infinite-dimensional linear flows there is a new type of trajectories that is absent in the finite-dimensional case.

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V. Zh. Sakbaev, I. V. Volovich. 2023-05-10. Analogues of Jacobi and Weyl Theorems for Infinite-Dimensional Tori. https://arxiv.org/abs/2305.05929

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