Abstract
In this chapter, we set a geometric framework for the study of differential equations and their symmetries. We reconduct differential equations to manifolds in an appropriate space, the jet space.1 The main difference from the familiar case of algebraic equations in R n are the relations existing between a function and its derivatives. In geometrical terms, these are taken care of by the natural contact structure with which the jet space is equipped.
Jet spaces were introduced by Ehresmann in the 1950s [120]; see e.g. [11,12,291]. The spaces of variables and their derivatives - very similar indeed to jet spaces - were already used by Lie, who introduced prolongations of vector fields.
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© 1999 Springer-Verlag Berlin Heidelberg
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(1999). Symmetry and Differential Equations. In: Symmetry and Perturbation Theory in Nonlinear Dynamics. Lecture Notes in Physics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48874-X_2
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DOI: https://doi.org/10.1007/3-540-48874-X_2
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Publisher Name: Springer, Berlin, Heidelberg
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