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The frozen-in condition for a direction field, small denominators and chaotization of steady flows of a viscous fluid

✍ Scribed by V.V. Kozlov

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 498 KB
Volume: 63
Category: Article
ISSN: 0021-8928
DOI: 10.1016/s0021-8928(99)00031-3

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✦ Synopsis

A clamical theorem of Heimhoitz states that vortex lines are frozen into a flow of barotropic ideal fluid in a potential force field. This result leads to the following general problem: it is required to find conditions under which a given dynamical system admils of a direction field frozen into its phase flow. By the rectification theorem for trajectories, a whole family of frozen direction fields always exLsts locally. It turns out that the problem of the existence of non-trivial fi'cgen direction fields defined in the whole phase space is closely related to the well-known problem of small denominators. Results of a general nature are applied to Hamiitonian systems, and also to steady flows of a viscous fluid.

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