55 citations · 486 across the 49 of their papers we have counts for
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A Lie systems approach for the first passage-time of piecewise deterministic processes
Florin Avram, José F. Cariñena, Javier de Lucas
Our paper illustrates how the theory of Lie systems allows recovering known results and provide new examples of piecewise deterministic processes with phase-type jumps for which th…
Superposition rules and second-order Riccati equations
J. F. Cariñena, J. de Lucas
A superposition rule is a particular type of map that enables one to express the general solution of certain systems of first-order ordinary differential equations, the so-called L…
Lie families: theory and applications
Jose F. Carinena, Janusz Grabowski, Javier de Lucas
We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expres…
Integrability of Lie systems through Riccati equations
José F. Cariñena, Javier de Lucas
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati…