Weakly mixing smooth planar vector field without asymptotic directions

Yuri Bakhtin, Liying Li

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a planar smooth weakly mixing stationary random vector field with nonnegative components such that, with probability 1, the flow generated by this vector field does not have an asymptotic direction. Moreover, for all individual trajectories, the set of partial limiting directions coincides with those spanning the positive quadrant. A modified example shows that a particle in space-time weakly mixing positive velocity field does not necessarily have an asymptotic average velocity.

Original languageEnglish (US)
Pages (from-to)4733-4744
Number of pages12
JournalProceedings of the American Mathematical Society
Volume148
Issue number11
DOIs
StatePublished - Nov 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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