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Gregory Reid - Deformations and symmetries of nonlinear differential systems
| GREGORY REID, Department of Applied Mathematics, University of Western Ontario London, Ontario |
| Deformations and symmetries of nonlinear differential systems |
Symbolic analysis, symmetries and deformations of differential systems are examined in several contexts.
Deformations of differential systems are related to the differential index which is a measure of the stability of the numerical solution of constrained systems of differential equations.
Nonlinear differential Lie systems are deformed to their corresponding linear differential systems by linearization about the identity map. Here the group is deformed to its Lie Algebra, with the homotopy from the Lie algebra to the Lie group being the exponentiation map.
Deformations under the toral group are scalings of the independent and dependent variables of differential systems. Nonlinear differential systems invariant under this group are classified, and their properties explored, in analogy to the Grobner Deformations of Sturmfels.
Some open questions regarding deformation as a generalization of the symmetry concept are also discussed.
Next: Pavel Winternitz - Nonlinear Up: II) Group Theory Methods and Previous: Jiri Patera - Non-standard
