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Dimension Theory Approach to the Complexity of Almost Periodic Trajectories. (arXiv:1710.03052v1 [math.DS])
来源于:arXiv
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. 查看全文>>