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

TL;DR

This paper extends the concept of lambda-symmetries to systems of first-order differential equations, demonstrating how these symmetries facilitate the reduction of such systems and comparing them with traditional Lie symmetries.

Contribution

It introduces the extension of lambda-symmetries to systems of first-order ODEs, providing a new method for reducing complex dynamical systems.

Findings

Lambda-symmetries enable reduction of first-order systems.

Comparison shows lambda-symmetries generalize Lie symmetries.

Examples illustrate practical application of the method.

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.