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This work presents a newly renovated approach to the analysis of second-orderRiccati equations from the point of view of the theory of Lie systems. We showthat these equations can be mapped into Lie systems through certain Legendretransforms. This result allows us to construct new superposition rules forstudying second-order Riccati equations and to reduce their integration tosolving (first-order) Riccati equations.Comment: 8 page

A NEW LIE–SYSTEMS APPROACH TO SECOND-ORDER RICCATI EQUATIONS