Analogues of Jacobi and Weyl Theorems for Infinite-Dimensional Tori
V. Zh. Sakbaev (1), I. V. Volovich (1) ((1) Steklov Mathematical, Institute of Russian Academy of Sciences)
TL;DR
This paper extends classical theorems about finite-dimensional linear flows to infinite-dimensional tori, exploring properties like periodicity, ergodicity, and discovering new trajectory types unique to infinite dimensions.
Contribution
It provides the first generalization of Jacobi and Weyl theorems to infinite-dimensional tori, including conditions for various dynamical behaviors and identifying novel trajectory types.
Findings
Conditions for periodicity and ergodicity established
New trajectory types identified in infinite-dimensional flows
Criteria for non-wandering and transitivity derived
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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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · advanced mathematical theories