Juan J. Morales-Ruiz
Professor of Mathematics
Campus Nord - Edifici OMEGA - Despatx 423
C/ Jordi Girona 1-3, 08034 Barcelona
Tels. 93 413 77 05
juan.morales-ruiz@upc.edu
Research
Publications and preprints
International Conference in Algebraic Methods in Dynamical Systems
Actual teaching
My interest is focused in the study of Dynamical Systems through Differential Galois Theory .
- Some recommended links:
Algebraic Methods in Dynamical Systems http://www-ma2.upc.edu/juan/amds.htm
Kolchin Seminar http://www.sci.ccny.cuny.edu/~ksda/
Research project Integrables Systems http://perso.univ-rennes1.fr/guy.casale/ANR/ANR_html/main.html
- Phd Students:
Primitivo Acosta Humánez
http://www-ma2.upc.edu/primi/
David Blázquez Sanz http://www-ma2.upc.edu/dblazquez/
Sergi Simón Estrada
Differential Galois Theory and Non-integrability
of Hamiltonian Systems, Progress
in Mathematics 179, Birkhäuser, Basel 1999. libroFSB.pdf
PAPERS AND PREPRINTS
Picard-Vessiot Theory and Ziglin's
Theorem (en colaboración con C. Simó),
Journal of Differential Equations 107 (1994) 140-162.
Bihamiltonian Systems and Lax Representation (en colaboración con R. Ramirez), Hamiltonian Mechanics: Integrability and Chaotic Behaviour, Ed. by J. Seimenis, Plenum Press, New York 1994, p. 253-259.
Non-integrability
criteria for Hamiltonians in the Case of Lamé Normal Variational Equations (en colaboración
con C. Simó), Journal of Differential Equations
129 (1996) 111-135.
On a Galosian Approach to the Splitting of Separatrices
(en colaboración con J. M. Peris),
Annales de la Faculté
des Sciences de Toulouse VIII (1999) 125-141. spli.pdf
Kovalevskaya, Liapounov, Painlevé, Ziglin and the
Differential Galois Theory, Regular and Chaotic Dynamics, 5
(2000) 251-272.kova.pdf
Galoisian obstructions to integrability
of Hamiltonian systems (en colaboración con J.P. Ramis), Methods and Applications of Analysis 8
(2001) 33-96. obsfin.pdf
Galoisian obstructions to integrability of Hamiltonian systems II (en colaboración con J.P. Ramis), Methods
and Applications of Analysis 8 (2001) 97-112.obs2fin.pdf
A Note of the Non-integrability of some Hamiltonian Systems with a
Homogeneous Potential (en colaboración con J.P. Ramis), Methods and Applications of Analysis 8
(2001) 113-120.homfin.pdf
On the Dynamical
meaning of the Picard-Vessiot Theory (en colaboración con J.M. Peris), Regular and Chaotic Dynamics 6(2001) 277-290. dy
gal.pdf
Meromorphic Nonintegrability of Hamiltonian Systems, Reports on Math. Physics 48 (2001) 183-194.
A Note on a
connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot
Theory, Banach Center Publications 58
(2002) 165-175. PAMfin.pdf
Meromorphic Nonintegrability of Hamiltonian
Systems I, Métodos de dinámica orbital y
rotacional, pag. 1-17, S. Ferrer, T. López Moratalla, A. Vigueras (Eds.), Univ. de
Murcia, Murcia 2002. Manga1.pdf
Meromorphic Nonintegrability of Hamiltonian
Systems II, Métodos de dinámica orbital y
rotacional, pag. 19-29, S. Ferrer, T. López Moratalla, A. Vigueras (Eds.), Univ. de
Murcia, Murcia 2002. Manga2.pdf
Review sobre el libro M. Singer, M. van der
Put, Galois
Theory of Linear Differential Equations, Springer 2003, Bulletin of the
AMS 41 (2004) 351-356. Review-Singer-Van der Put book.pdf
Algebraic
proof of the Non-integrability of Hill’s Problem (en colaboración con C. Simó y S.
Simon), Ergodic
Theory and Dynamical Systems 25 (2005) 1237-1256.hill .pdf
A Remark
about the Painlevé Transcendents,
proceedings
Integrability of Hamiltonian
Systems and Differential Galois Groups of Higher Variational
Equations (en colaboración con J. P. Ramis y C. Simó), preprint,
aceptado en Ann. Sc. Ec. Norm. Sup. hvariatio-fin.pdf
Integrability of Dynamical Systems
through Differential Galois Theory: a practical guide (en colaboración
con J.-P Ramis), preprint.
·
Actual teaching
Cálculo, Ingeniería Informática.