Javier de Lucas Araujo
Assistant professor at University of
Warsaw
Department of Mathematical Methods in
Physics (KMMF)
ul. Pasteura 5, 02-093, Warsaw, POLAND.
Fields
of Interes
Geometric Methods in Mathematics and Physics.
Contact, Presymplectic, Symplectic, k-symplectic, Poisson, Jacobi,
multisymplectic and Dirac Geometry.
Geometry of differential equations
Discrete Vakonomic Mechanics
Riemmanian and Kahler geometry
Lie algebroids and supermanifolds
Geometric Quantum Mechanics and BRST
Collaborators
J. Grabowski (IMPAN, Poland)
C. Sardón (University of Salamanca, Spain)
J.F. Cariñena (University of Zaragoza and IUMA, Spain)
E. Martínez (University of Zaragoza and IUMA, Spain)
M.F. Rañada (University of Zaragoza and IUMA, Spain)
A. Ramos (University of Zaragoza, Spain)
S. Vilariño (Centro Universitario de la Defensa de
Zaragoza and IUMA, Spain)
A. Blasco (University of Burgos, Spain)
A. Ballesteros (University of Burgos, Spain)
F.J. Herranz (University of Burgos, Spain)
Y.M. Vorobjev (University of Hermosillo, Mexico)
R. Flores-Espinoza (University of Hermosillo, Mexico)
G. Marmo (University Federico III, Italy)
J. Jover (University of Zaragoza, Spain)
J. Clemente-Gallardo (University of Zaragoza, Spain)
P. Guha (S.N. Bose National Centre for Basic Sciences,
India)
M. Kus (Center for Theoretical Physics of the Polish
Academy of Science, Poland)
S. Charzynski (Department of the Mathematics of the Polish
Academy of Science, Poland)
M. Tobolski (University of Warsaw, Poland)
A.M. Grundland (University troj Riviera and CRM, Canada)
P. Winternitz (University of Montreal and CRM, Canada)
Publications
Times cited 234
Citing articles 79
Average citations per item 7.31
h-index 9
- P.G. Estevez, F.J. Herranz, J. de Lucas and C.
Sardón, Lie symmetries for Lie systems:
applications of ODEs and HODEs.
To appear in Applied Mathematics and Computation[Arxiv]
- A. Blasco, F.J. Herranz, J. de Lucas and C. Sardõn
"Lie--Hamilton systems on the plane: applications and superposition rules"
J. Phys. A 48, 345202 (2015)[Arxiv]
- J.F. Cari\~nena, J. de Lucas and M.F. Rañada,
"Jacobi multipliers, nonlocal symemtries and harmonic oscillators" J. Math. Phys.
56, 063505 (2015).
- J.F. Cariñena and J. de Lucas, Quasi-Lie
families, quasi-Lie schemes, and their applications
to Abel equations.
J. Math. Anal. Appl. 430, 648--671 (2015).
- F.J. Herranz, J. de Lucas and C. Sardõn "Jacobi--Lie
systems: theory and low dimensional classification"
Accepted in Proceedings AIMS (2015). [Arxiv]
- J. de Lucas, M. Tobolski and S. Vilarino A new application of $k$-symplectic Lie systems. Int. J. Geom. Methods Mod. Phys. 1550071 (2015). [Arxiv]
- J. de Lucas and S. Vilariño, k-symplectic Lie
systems: theory and applications. J. Differential Equations 258 (6), 2221--2255 (2015).[Arxiv]
- A. Ballesteros, A. Blasco, J.F. Herranz, J. de Lucas
and C. Sardõn, Lie-Hamilton systems on the plane:
theory, classification and applications.
J. Differential Equations 258, 2873--2907 (2015).[Arxiv]
- J.F. Cariñena, J. Grabowski, J. de Lucas and C. Sardón, Dirac--Lie
systems and Schwarzian equations.J. Differential Equations 257 (7), 2303--2340 (2014)[Arxiv]
- A. Ballesteros, J.F. Cariñena, F.J.
Herranz, J. de Lucas and C. Sardón, From constants of
motion to superposition rules for Lie--Hamilton systems.
J. Phys. A: Math. Theor. 46, 285203 (2013).[Arxiv]
- J. de Lucas and C. Sardón, On Lie
systems and Kummer--Schwarz equations. J.
Math. Phys. 54, 033505 (2013).[Cites:1][Arxiv]
- J.F. Cariñena, J. de
Lucas and C. Sardón, Lie--Hamilton systems: theory
and applications, [Cited:1] Int. J. Geom.
Methods Mod. Phys. 10, 09129823 (2013).[Arxiv]
- J.F.
Cariñena, J. de Lucas and P. Guha, A quasi-Lie
schemes approach to the Gambier equation.
SIGMA 9, 026 (2013).[Arxiv]
- J. Grabowski and J. de Lucas, Mixed
superposition rules and the Riccati hierarchy.
J. Diff. Equ. 254, 179--198 (2013). [cites:2][Arxiv]
- J.F. Cariñena, J. de Lucas and J.
Grabowski, Superposition rules for higher-order
systems and their applications, J.
Phys. A: Math. Theor. 45, 185202 (2012). [Cites:5][Arxiv]
- 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).
- 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).[Cites:4]
[Arxiv] [MathSci]
- J.F. Cariñena and J. de Lucas, Superposition
rules and second-order Riccati equations, J.
Geom. Mech. 3, 1--22, 2011.[Cites:12] [Arxiv] [MathScinet]
- J.F. Cariñena and J. de Lucas, Lie
systems: theory, generalizations, and applications,
Dissertationes Math. 479, 2011.[Cites: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] [Cites:2]
- 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]
- J.F. Cariñena and J. de Lucas, Integrability of Lie systems
through Riccati equations, J.
Nonl. Math. Phys. 18, 29--54 (2011).
[Cites:2][Arxiv]
[MathScinet]
- 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). [Cites:5][Arxiv] [MathScinet]
- 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]
- J.F. Cariñena, J. Grabowski and J. de
Lucas, Lie families:
theory and applications, J.
Phys. A 43 305201 (2010). [Cites:4]Arxiv:1003.3529
[MathScinet]
- R. Flores, J. de Lucas and Y. Vorobiev,
Phase splitting for
periodic Lie systems, J. Phys
A. 43, 205208 (2010). Arxiv:0910.2575[Cites:6]
[MathScinet]
- 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[Cites:5]
[MathScinet]
- 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[Cites:6]
- 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[Cites:6]
- J.F. Cariñena, J. Grabowski and J. de
Lucas, Quasi-Lie
schemes: theory and applications, J.
Phys. A 42, 335206 (2009). Arxiv:0810.1160
[Cites:10]
- 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
[Cites:14]
- 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[Cites:7]
- 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
[Cites:No data]
- 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[Cites:25]
- 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[Cites:9]
- 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[Cites:16]
- 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[Cites:No
data]
- 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
[Cites:No data]
Preprints and works in
progress
J. de Lucas, M. Tobolski and S. Vilariño,
"Octonionic Riccati equations", Submitted to J. Math. Anal. Appl.
J.F. Cari\~nena, J. Clemente-Gallardo, J. de Lucas
and J. Jover, "Kahler Lie systems and quantum systems"
To be submitted to J. Diff. Equ.
J.F. Cariñena, J. de Lucas and C. Sardon, Quasi-Lie
schemes in quantum mechanics. To be submitted to J. Phys. A
A.M. Grundland and J. de Lucas, A Lie systems approach to the Riccati hierarchy and PDEs, To be submitted
J. Grabowski and J. de Lucas, Grassmann valued
differential equations and applications,
J.F. Cariñena, G. Marmo and J. de Lucas, Iso-purity
solutions of non-Hamiltonian Lie systems.
J.F. Cari\~nena, S. Charzy\'nski, J. de Lucas and M.
Ku\'s, Characterization of linear systems of
Wei--Norman type and applications to birth-death
processes
Other works
Referee for the Portuguese Foundation for Science
and Technology
Referee for J. Phys. A, Adv. Math. Phys., Rep. Math.
Phys., Journal of Dynamical and Control Systems,
Annals of Physics, Proceedings of the Royal Society A,
International Journal Geometric Methods in Modern
Physics, Advances in Mathematical Physics, and others
Reviewer for ZentralBlatt Public
profile
Reviewer for Mathematical Reviews Public
profile
Organization
Organizator of the Meeting
on Lie systems: theory, generalizations and applications
(with J. Grabowski) Web
page
Docent work
- PhD Supervisor of Cristina Sardon (University of
Salamanca, Spain)
- Master thesis supervisor of Mariola Napiorkowska
(UKSW, Poland)
- Master thesis supervisor of Katarzyna Prokopiuk (UKSW,
Poland)
- Dyplom thesis supervisor of Mariusz Tobolski (UW, Poland)
- Dyplom thesis supervisor of Daniel Wysocki (UW, Poland),
Poland)
OFERTA PRAC
MAGISTERSKICH/LICENCJARSKICH
- Oferty prac magisterskich/licencjarskich na UWOpis
