Integrability of Lie Systems through Riccati Equations
- https://doi.org/10.1142/S1402925111001131How to use a DOI?
- Lie–Scheffers systems, Riccati equations, integrability conditions
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyze a geometric method to construct integrability conditions for Riccati equations following these approaches. Our procedure provides us with a unified geometrical viewpoint that allows us to analyze some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalized to describe integrability conditions for any Lie system. Finally we show the usefulness of our treatment in order to study the problem of the linearizability of Riccati equations.
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - José F. Cariñena AU - Javier de Lucas PY - 2021 DA - 2021/01 TI - Integrability of Lie Systems through Riccati Equations JO - Journal of Nonlinear Mathematical Physics SP - 29 EP - 54 VL - 18 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001131 DO - https://doi.org/10.1142/S1402925111001131 ID - Cariñena2021 ER -