Reduction of systems of first-order differential equations via Lambda-symmetries

Abstract

The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type produces a reduction of the differential equations, restricting the presence of the variables involved in the problem. The results are compared with the case of standard (i.e. exact) Lie-point symmetries and are also illustrated by some examples.

12 pages

References in corpus (5)

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• On the relation between standard and $\mu$-symmetries for PDEs
• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Noether theorem for mu-symmetries
• On the notion of conditional symmetry of differential equations

Cited by in corpus (8)

• Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations
• A gauge-theoretic description of $\mu$-prolongations, and $\mu$-symmetries of differential equations
• Dynamical systems and σ-symmetries
• On the connections between symmetries and conservation rules of dynamical systems
• Integration of differential equations by ${\mathcal{C}}^{\infty }$-structures
• Symmetry and Lie-Frobenius reduction of differential equations
• Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations
• On the Geometry of Twisted Symmetries: Gauging and Coverings