Juan J. Morales-Ruiz

Catedrático de Universidad (Professor of Mathematics)

Universidad Politécnica de Madrid

Escuela Superior de Ingenieros de Caminos, Canales y Puertos

c/ Profesor Aranguren, s/n - 28040 Madrid

Tels. 91 336 66 66

juan.morales-ruiz@upm.es

 

Research

            Publications and preprints

            International Conference in Algebraic Methods in Dynamical Systems

            

 


  • Research

         My interest is focused in the study of Dynamical Systems and Mathematical Physics through Differential Galois Theory.

    - Some links:          

         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://ima.usergioarboleda.edu.co/Primi.htm

David Blázquez Sanz   http://www.usergioarboleda.edu.co/matematicas/dblazquez

                  Sergi Simón Estrada  http://www.port.ac.uk/departments/academic/maths/staff/title,92184,en.html

  •   Publications and preprints

BOOKS

Differential Galois Theory and Non-integrability of Hamiltonian Systems, Progress in Mathematics 179, Birkhäuser, Basel 1999. libroFSB.pdf

 

SOME PAPERS AND PREPRINTS

 

On a Galosian Approach to the Splitting of Separatrices (with 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 (with J.P. Ramis), Methods and Applications of Analysis 8 (2001) 33-96. obsfin.pdf

Galoisian obstructions to integrability of Hamiltonian systems II (with 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 (with J.P. Ramis), Methods and Applications of Analysis 8 (2001) 113-120.homfin.pdf

On the Dynamical meaning of the Picard-Vessiot Theory (with J.M. Peris), Regular and Chaotic Dynamics 6(2001) 277-290. dy gal.pdf

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

Review on the book 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 (with C. Simó and  S. Simon),  Ergodic Theory and Dynamical Systems 25 (2005) 1237-1256.hill .pdf

A Remark about the Painlevé Transcendents Theories asymptotiques et equations de Painlevé, Universidad de Angers, Angers, Francia 2004. Painlevefin.pdf

Integrability of Hamiltonian Systems and Differential Galois Groups of Higher Variational Equations (with J. P. Ramis and C. Simó), Ann. Sc. Ec. Norm. Sup. 40 (2007) 845-884. hvariatio-fin.pdf

 

On the meromorphic non-integrability of some N-body problems (with S. Simón), Discrete and Continuous Dynamical Systems 24 (2009) 1225 - 1273.

Simofestfinal.pdf

 

Integrability of Dynamical Systems through Differential Galois Theory: a practical guide (with J.-P Ramis),

Differential algebra, complex analysis and orthogonal polynomials, 143–220, Contemp. Math., 509, Amer. Math. Soc., Providence, RI, 2010. raiz-libhand.pdf

 

Differential Galois theory of algebraic Lie-Vessiot systems (with D. Blázquez-Sanz),  Differential algebra, complex analysis and orthogonal polynomials, 1–58, Contemp. Math. 509,  Amer. Math. Soc., Providence, RI, 2010. Blazquez-Morales diff arxiv  0901.4480.pdf

 

 Local and global aspects of Lie superposition theorem (with D. Blázquez-Sanz),   J. Lie Theory 20 (2010) 483–517.Blazquez-Morales lg arxiv 0901.4478.pdf

 

 Galoisian Approach to integrability of Schrödinger Equation (with P.-B. Acosta-Humánez and J.-A. Weil), Reports on Mathematical Physics 67 (2011) 305- 374 Acosta-Morales-Weil arxiv 1008.3445.pdf

 

 Lie’s reduction method and differential Galois theory in the complex analytic context (with D. Blázquez-Sanz),   Discrete Contin. Dyn. Syst.  32 (2012)353-379.Blazquez-Morales liered arxiv 0901.4479.pdf

 

On the integrability of polynomial fields in the plane by means of Picard-Vessiot Theory (with P.-B. Acosta-Humánez, J.-T.Lázaro and C. Pantazi). Preprint, 2012. Acosta_Lazaro_Morales_Pantazi arxiv 1012.4796.pdf