University of Warwick
MacKay R. S.
Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow
2018, vol. 23, no. 6, pp. 797-802
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.