Synchronization properties of random piecewise isometries
Anton Gorodetski, Victor Kleptsyn
TL;DR
This paper investigates the synchronization behavior of random double rotations on tori, establishing criteria for synchronization on the circle and proving its absence in higher dimensions.
Contribution
It introduces a criterion for synchronization in random double rotations on the circle and demonstrates that synchronization does not occur in dimensions two and above.
Findings
Synchronization occurs under specific conditions on the circle.
Synchronization is always absent in dimensions two and higher.
Provides theoretical criteria for synchronization in random dynamical systems.
Abstract
We study the synchronization properties of the random double rotations on tori. We give a criterion that show when synchronization is present in the case of random double rotations on the circle and prove that it is always absent in dimensions two and higher.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation