A generalization of λ-symmetry reduction for systems of ODEs: σ-symmetries

Abstract

We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the "invariants by differentiation" property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries.

32 pages

References in corpus (2)

• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Noether theorem for mu-symmetries

Cited by in corpus (7)

• ${\mathcal{C}}^{\infty }$-symmetries of distributions and integrability
• Dynamical systems and σ-symmetries
• Integration of differential equations by ${\mathcal{C}}^{\infty }$-structures
• Symmetry and Lie-Frobenius reduction of differential equations
• ${\mathcal{C}}^{\infty }$-structures in the integration of involutive distributions
• Generalized notions of symmetry of ODE's and reduction procedures
• On the Geometry of Twisted Symmetries: Gauging and Coverings