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Synchronization Properties of Random Piecewise Isometries

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, CA, 92697, USA

    Anton Gorodetski

  2. CNRS, Institute of Mathematical Research of Rennes, IRMAR, UMR 6625 du CNRS, Rennes, France

    Victor Kleptsyn

Authors
  1. Anton Gorodetski
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  2. Victor Kleptsyn
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Corresponding author

Correspondence to Anton Gorodetski.

Additional information

Communicated by K. Khanin

V. K. was supported in part by RFBR project 13-01-00969-a and RFBR/CNRS joint project 10-01-93115-CNRS_a.

A. G. was supported in part by NSF grants DMS-1301515 and IIS-1018433.

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Gorodetski, A., Kleptsyn, V. Synchronization Properties of Random Piecewise Isometries. Commun. Math. Phys. 345, 781–796 (2016). https://doi.org/10.1007/s00220-016-2678-8

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