@article{12, keywords = {converse KAM theory, conefields, volume-preserving, Hamiltonian}, author = {Robert MacKay}, title = {Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow}, 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{\textendash}Arnol{\textquoteright}d Hamiltonian flows and for boundaryless submanifolds.

}, year = {2019}, journal = {Regular and Chaotic Dynamics}, volume = {27}, chapter = {797}, month = {12/2018}, url = {https://doi.org/10.1134/S1560354718060126}, doi = {10.1134/S1560354718060126}, language = {eng}, }