Integrability of Lie systems through Riccati equations

Abstract

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.

Corrected typos

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Cited by in corpus (4)

• k-symplectic Lie systems: theory and applications
• Explicit solutions of the ${\mathfrak{a}}_1$-type Lie-Scheffers system and a general Riccati equation
• A Lie systems approach for the first passage-time of piecewise deterministic processes
• On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation