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A relationship between jacobian maps and the commutativity properties of suitable couples of hamiltonian vector fields is studied. A theorem by Meisters and Olech is extended to the nonpolynomial case. A property implying the Jacobian Conjecture in ℝ² is described.
M. Sabatini. "Commutativity of flows and injectivity of nonsingular mappings." Annales Polonici Mathematici 76.1-2 (2001): 159-168. <http://eudml.org/doc/280388>.
@article{M2001, abstract = {A relationship between jacobian maps and the commutativity properties of suitable couples of hamiltonian vector fields is studied. A theorem by Meisters and Olech is extended to the nonpolynomial case. A property implying the Jacobian Conjecture in ℝ² is described.}, author = {M. Sabatini}, journal = {Annales Polonici Mathematici}, keywords = {nonsingular mappings; Jacobian maps; plane Hamiltonian systems; Jacobian conjecture; real plane}, language = {eng}, number = {1-2}, pages = {159-168}, title = {Commutativity of flows and injectivity of nonsingular mappings}, url = {http://eudml.org/doc/280388}, volume = {76}, year = {2001}, }
TY - JOUR AU - M. Sabatini TI - Commutativity of flows and injectivity of nonsingular mappings JO - Annales Polonici Mathematici PY - 2001 VL - 76 IS - 1-2 SP - 159 EP - 168 AB - A relationship between jacobian maps and the commutativity properties of suitable couples of hamiltonian vector fields is studied. A theorem by Meisters and Olech is extended to the nonpolynomial case. A property implying the Jacobian Conjecture in ℝ² is described. LA - eng KW - nonsingular mappings; Jacobian maps; plane Hamiltonian systems; Jacobian conjecture; real plane UR - http://eudml.org/doc/280388 ER -