Aperiodic Sequences and Aperiodic Geodesics
Viktor Schroeder, Steffen Weil

TL;DR
This paper introduces a quantitative measure of aperiodicity in dynamical systems and demonstrates the existence of highly aperiodic sequences and geodesics in specific mathematical settings.
Contribution
It defines a new quantitative condition for aperiodicity and proves the existence of maximally aperiodic sequences and geodesics under this condition.
Findings
Existence of maximally aperiodic sequences in Bernoulli-shift
Existence of maximally aperiodic geodesics on hyperbolic manifolds
Quantitative measure effectively captures aperiodicity
Abstract
We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as possible with respect to this condition.
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