Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 002, 18 pages      arXiv:2306.13175      https://doi.org/10.3842/SIGMA.2024.002
Contribution to the Special Issue on Symmetry, Invariants, and their Applications in honor of Peter J. Olver

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

Peter Rock
Department of Mathematics, University of Colorado Boulder, 395 UCB, Boulder, CO 80309, USA

Received July 04, 2023, in final form December 29, 2023; Published online January 02, 2024

Abstract
This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], 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.

Key words: jet space; multispace; symmetry methods; differential equations; numerical ordinary differential equations.

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