Juan J. Morales-Ruiz

Professor of Mathematics

Universitat Politècnica de Catalunya

Departament MA II

Campus Nord - Edifici OMEGA - Despatx 423
C/ Jordi Girona 1-3, 08034 Barcelona
Tels. 93 413 77 05
juan.morales-ruiz@upc.edu

 

Research

Curriculum vitae

            Publications and preprints

            International Conference in Algebraic Methods in Dynamical Systems

            Actual teaching

 


  • Research

         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

BOOKS

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 del congreso Theories asymptotiques et equations de Painlevé, Universidad de Angers, Angers, Francia 2004, preprint, aceptado. Painlevefin.pdf

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.