Dimension Theory Approach to the Complexity of Almost Periodic Trajectories
Dynamical Systems
2017-10-10 v1 Number Theory
Abstract
We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine dimension is connected with recurrent and ergodic properties of an almost periodic function. We get some estimates of the Diophantine dimension for certain quasiperiodic functions and present methods to investigate such a characteristic for almost periodic trajectories of evolution equations. Also we discuss the link between the presented approach and the so called effective versions of the Kronecker theorem.
Keywords
Cite
@article{arxiv.1710.03052,
title = {Dimension Theory Approach to the Complexity of Almost Periodic Trajectories},
author = {Mikhail Anikushin},
journal= {arXiv preprint arXiv:1710.03052},
year = {2017}
}