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

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. [ABSTRACT FROM AUTHOR]