Javier de Lucas Araujo

Collaborators

Publications

1. J. Grabowski and J. de Lucas, Mixed superposition rules and the Riccati hierarchy. To appear in J. Diff. Equ. (2012). [Arxiv]
2. J.F. Cariñena, J. de Lucas and J. Grabowski, Superposition rules, higher-order systems and their applications, J. Phys. A: Math. Theor. 45, 185202 (2012). [Arxiv]
3. J.F. Cariñena, J. de Lucas and M.F. Rañada, Un enfoque geometrico de las ecuaciones diferenciales de Abel de primera y segunda clase, Actas del XI Congreso del Dr. Antonio Monteiro 2011, 63--82 (2012).
4. J.F. Cariñena, J. de Lucas and C. Sardón, A new Lie systems approach to second-order Riccati equations, Int. J. Geom. Methods Mod. Phys. 9, 1260007 (2012). [Arxiv] [MathSci]
5. J.F. Cariñena and J. de Lucas, Superposition rules and second-order Riccati equations, J. Geom. Mech. 3, 1--22, 2011. [Arxiv] [MathScinet]
6. J.F. Cariñena and J. de Lucas, Lie systems: theory, generalizations, and applications, Dissertationes Math. 479, 2011.
7. J.F. Cariñena and J. de Lucas, Superposition rules and second-order differential equations, in the book: XIX International Fall Workshop on Geometry and Physics, AIP Conference Proceedings 1360, American Institute of Mathematics, 2011, 127--132. [Arxiv]
8. P.G. Estevez, M.L. Gandarias and J. de Lucas, Classical Lie symmetries and reductions of a nonisospectral Lax pair, J. Nonlinear Math. Phys. 18, 51--60 (2011). [Arxiv] [MathScinet]
9. J.F. Cariñena and J. de Lucas, Integrability of Lie systems through Riccati equations, J. Nonl. Math. Phys. 18, 29--54 (2011). [Arxiv] [MathScinet]
10. J.F. Cariñena, J. de Lucas and M.F. Rañada, A geometric approach to integrability of Abel differential equations, Int. J. Theor. Phys. 50, 2114-2124 (2011). [Arxiv] [MathScinet]
11. F. Avram, J.F. Cariñena and J. de Lucas, A Lie systems approach for the first passage-time of piecewise deterministic processes, in the book: Modern Trends of Controlled Stochastic Processes: Theory and Applications, pp. 144-160 (A.B.Piunovskiy ed), Luniver Press, 2010. [Arxiv] [MathScinet]
12. J.F. Cariñena, J. Grabowski and J. de Lucas, Lie families: theory and applications, J. Phys. A 43 305201 (2010). Arxiv:1003.3529 [MathScinet]
13. R. Flores, J. de Lucas and Y. Vorobiev, Phase splitting for periodic Lie systems, J. Phys A. 43, 205208 (2010). Arxiv:0910.2575 [MathScinet]
14. J.F. Cariñena, J. de Lucas and M.F. Rañada, Lie systems and integrability conditions for t-dependent frequency harmonics oscillators, Int. J. Geom. Methods Mod. Phys. 7, 289--310 (2010). Arxiv:0908.2292 [MathScinet]
15. J.F. Cariñena and J. de Lucas, Quantum Lie systems and integrability conditions, Int. J. Geom. Meth. Mod. Phys. 6, 1235--1252 (2009). Arxiv:0908.2292
16. J.F. Cariñena, P.G.L. Leach and J. de Lucas, Quasi-Lie schemes and Emden--Fowler equations, J. Math. Phys. 50, 103515 (2009) Arxiv:0908.2292
17. J.F. Cariñena, J. Grabowski and J. de Lucas, Quasi-Lie schemes: theory and applications, J. Phys. A 42, 335206 (2009). Arxiv:0810.1160
18. J.F. Cariñena and J. de Lucas, Applications of Lie systems in dissipative Milne--Pinney equations, Int. J. Geom. Meth. Modern Phys. 6, 683--699 (2009). Arxiv:0902.2132
19. J.F. Cariñena, J. de Lucas and A. Ramos, A geometric approach to time evolution operators of Lie quantum systems, Int. J. Theor. Phys. 48, 1379--1404 (2009). Arxiv:0811.4386
20. J.F. Cariñena and J. de Lucas, Lie systems and integrability conditions of differential equations and some of its applications, Proceedings of the 10th international conference on differential geometry and its applications. Arxiv:0902.1135
21. J.F. Cariñena, J. de Lucas and M.F. Rañada, Recent Applications of the Theory of Lie Systems in Ermakov Systems, SIGMA 4, 031 (2008). Arxiv:0803.1824
22. J.F. Cariñena, J. de Lucas and M.F. Rañada, Integrability of Lie systems and some of its applications in physics, J. Phys. A 41, 304029 (2008). Arxiv:0810.4006
23. J.F. Cariñena and J. de Lucas, A nonlinear superposition rule for solutions of the Milne--Pinney equation, Phys. Lett. A 372, 5385--5389 (2008). Arxiv:0807.0370
24. J.F. Cariñena, J. de Lucas and A. Ramos, A geometric approach to integrability conditions for Riccati equations, Electronic Journal of Differential Equations 122, 1--14 (2007). Arxiv:0810.1740
25. J.F. Cariñena, J. de Lucas and Manuel F. Rañada, Nonlinear superpositions and Ermakov systems, in the book: Differential Geometric Methods in Mechanics and Field Theory, pp.15--33, eds F. Cantrijn, M. Crampin and B. Langerock, Academia Press, Prague, 2007. Arxiv:0810.3494

Preprints and works in progress