0
2013
Impact Factor

Peter Olver

127 Vincent Hall, 206 Church St. S.E., MN 55455, Minneapolis, USA
School of Mathematics, University of Minnesota

Publications:

Mari Beffa  G., Olver P. J.
Poisson structures for geometric curve flows in semi-simple homogeneous spaces
2010, vol. 15, no. 4-5, pp.  532-550
Abstract
We apply the equivariant method of moving frames to investigate the existence of Poisson structures for geometric curve flows in semi-simple homogeneous spaces. We derive explicit compatibility conditions that ensure that a geometric flow induces a Hamiltonian evolution of the associated differential invariants. Our results are illustrated by several examples of geometric interest.
Keywords: moving frame, Poisson structure, homogeneous space, invariant curve flow, differential invariant, invariant variational bicomplex
Citation: Mari Beffa  G., Olver P. J.,  Poisson structures for geometric curve flows in semi-simple homogeneous spaces, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 532-550
DOI:10.1134/S156035471004009X
Kim P., Olver P. J.
Geometric integration via multi-space
2004, vol. 9, no. 3, pp.  213-226
Abstract
We outline a general construction of symmetry-preserving numerical schemes for ordinary differential equations. The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis. We explain how to invariantize standard numerical integrators such as the Euler and Runge–Kutta schemes; in favorable situations, the resulting symmetry-preserving geometric integrators offer significant advantages.
Citation: Kim P., Olver P. J.,  Geometric integration via multi-space, Regular and Chaotic Dynamics, 2004, vol. 9, no. 3, pp. 213-226
DOI:10.1070/RD2004v009n03ABEH000277
Olver P. J.
Moving Frames and Joint Differential Invariants
1999, vol. 4, no. 4, pp.  3-18
Abstract
This paper surveys the new, algorithmic theory of moving frames developed by the author and M.Fels. The method is used to classify joint invariants and joint differential invariants of transformation groups, and equivalence and symmetry properties of submanifolds. Applications in classical invariant theory, geometry, and computer vision are indicated.
Citation: Olver P. J.,  Moving Frames and Joint Differential Invariants, Regular and Chaotic Dynamics, 1999, vol. 4, no. 4, pp. 3-18
DOI:10.1070/RD1999v004n04ABEH000131

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