Juan J. Morales-Ruiz
Catedrático
de Universidad (Professor of
Mathematics)
c/ Profesor Aranguren, s/n - 28040 Madrid
Tels. 91 336 66 66
Research
Publications and preprints
International Conference in Algebraic Methods in Dynamical Systems
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
Differential Galois Theory and Non-integrability
of Hamiltonian Systems, Progress
in Mathematics 179, Birkhäuser,
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,
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
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.,
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.,
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