A note on Bohr chaos and hyperbolic sets
Noriaki Kawaguchi
TL;DR
This paper explores the connection between shadowing phenomena and Bohr chaos in dynamical systems, providing conditions that link these concepts and revealing structural properties of hyperbolic sets.
Contribution
It introduces new sufficient conditions for Bohr chaos based on shadowing, enhancing understanding of hyperbolic sets in dynamical systems.
Findings
Established conditions linking shadowing and Bohr chaos
Derived results on hyperbolic sets using shadowing lemma
Highlighted structural properties of hyperbolic sets
Abstract
This paper studies the relationship between shadowing phenomena and Bohr chaos in dynamical systems. We provide sufficient conditions for Bohr chaos in terms of shadowing. By combining those conditions with the shadowing lemma, we obtain some results on Bohr chaos and hyperbolic sets. Our results also highlight some simple but non-trivial structural properties of hyperbolic sets.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stability and Controllability of Differential Equations · Quantum chaos and dynamical systems