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Rotation of trajectories of lipschitz vector fields

Georges Comte Universite de Nice Sophia-Antipolis Yosef Yomdin the Weizmann Institute of Science

Differential Geometry mathscidoc:1609.10108

Journal of Differential Geometry, 81, (3), 601-630, 2009
We prove that the rotation in time T of a trajectory of a K-Lipschitz vector ¯eld in Rn around a given point (stationary or non-stationary) is bounded by A + BKT with A;B absolute constants. In particular, trajectories of a Lipschitz vector ¯eld in ¯nite time cannot have an in¯nite rotation around a given point (while trajectories of a C1 vector ¯eld may have an in¯- nite rotation around a straight line in ¯nite time). The bound above extends to the mutual rotation of two trajectories (for the time intervals T and T0, respectively) of a K-Lipschitz vector ¯eld in R3: this rotation is bounded from above by the quantity CK min(T; T0) + DK2TT0.
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@inproceedings{georges2009rotation,
  title={ROTATION OF TRAJECTORIES OF LIPSCHITZ VECTOR FIELDS},
  author={Georges Comte, and Yosef Yomdin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911180902673806765},
  booktitle={Journal of Differential Geometry},
  volume={81},
  number={3},
  pages={601-630},
  year={2009},
}
Georges Comte, and Yosef Yomdin. ROTATION OF TRAJECTORIES OF LIPSCHITZ VECTOR FIELDS. 2009. Vol. 81. In Journal of Differential Geometry. pp.601-630. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911180902673806765.
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