Regular and Chaotic Dynamics

, Volume 23, Issue 6, pp 797–802 | Cite as

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

  • Robert S. MacKayEmail author


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.


converse KAM theory conefields volume-preserving Hamiltonian 

MSC2010 numbers

37J30 70H07 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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