Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable

Author:

Peter Rock

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-21 16:00:00

Abstract

This work expands upon the paper Geometric Foundations of Numerical Algorithms and Symmetry by Peter Olver wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally, and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space.

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