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Regular and Chaotic Dynamics, 2018, Volume 23, Issue 6, Pages 797–802
DOI: https://doi.org/10.1134/S1560354718060126 (Mi rcd367) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow

Robert S. MacKay

Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, U.K.
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DOI: https://doi.org/10.1134/S1560354718060126
Abstract: A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan–Arnol’d Hamiltonian flows and for boundaryless submanifolds.
Keywords: converse KAM theory, conefields, volume-preserving, Hamiltonian.
Funding agency Grant number
Simons Foundation 601970
National Science Foundation DMS-1440140
This work was supported partly by a grant from the Simons Foundation/SFARI (601970, RSM) and partly by the National Science Foundation under Grant No. DMS-1440140, while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2018 semester.
Received: 08.09.2018
Accepted: 02.11.2018
Bibliographic databases:
Document Type: Article
MSC: 37J30, 70H07
Language: English
Citation: Robert S. MacKay, “Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow”, Regul. Chaotic Dyn., 23:6 (2018), 797–802
Citation in format AMSBIB
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\by Robert S. MacKay
\paper Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 6
\pages 797--802
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    • This publication is cited in the following 9 articles:
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