Symmetries and infinitesimal symmetries of singular differential equations

Details Symmetries and infinitesimal symmetries of singular differential equations Symmetries and infinitesimal symmetries of singular differential equations

2002-01-16

arxiv.org/abs/math-ph/0201034v1

Physics

Mathematical Physics

22 pages

Scientific paper

10.1088/0305-4470/35/24/306

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of geometric symmetry of a linearly singular differential equation is introduced as a transformation that preserves the geometric data that define the problem. It is proved that such symmetries are essentially equivalent to dynamic symmetries, that is, transformations mapping solutions into solutions. Similar results are given for infinitesimal symmetries. To study the invariance of several objects under the flows of vector fields, a careful study of infinitesimal variations is performed, with a special emphasis on infinitesimal vector bundle automorphisms.

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