Alexey GLUTSYUK

Researcher at the Laboratory since January 2005

Permanent place of employment

Unité de Mathématiques Pures et Appliquées, M.R., École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon 07, France

Research interests:

Dynamical systems, group actions by diffeomorphisms, foliations by Riemann surfaces, uniformization.

Research Seminars and Conferences (some titles are approximate):

• Conference "Topological and geometric methods of complex differential equations" - RIMS, Kyoto, January 19-23, 2004.
• Conference "Bifurcations, cycles limites et feuilletages analytiques" in honour of Robert Roussarie's 60-th birthday (CIRM, Marseille-Luminy, June 7-11, 2004).
• Conference "Lyapunov Exponents and related topics in dynamics and geometry" (Moscow, January 24-28, 2005)
• Conference "Dynamics and Chaos" (in honour of L.P.Shilnikov's 70-th birthday, Nizhny Novgorod, January 31- February 4 2005).

Recent publications

1. On simultaneous uniformization and local nonuniformizability. - C.R.Acad.Sci.Paris, Série 1 Math., t.334 (2002), p.489-494.
2. Resonant confluence of singular points and Stokes phenomena. - Journal of Dynamical and Control Systems, vol. 10 (2004), No. 2 (April), pp. 253--302.
3. Simultaneous metric uniformization of foliations by Riemann surfaces" - Commentarii Mathematici Helvetici, vol. 79, Issue 4 (2004), pp.704-752.
4. On the monodromy group of confluenting linear equations. - To appear in Moscow Mathematical Journal. http://xxx.lanl.gov/abs/math.DS/0304243.

Proceedings of conferences

Confluence of singular points and Stokes phenomena. - Proceedings of NATO Advanced Study Institute "Normal Forms, Bifurcations and Finiteness Problems in Differential Equations", Montreal July 6-19 2002 (C. Rousseau and Yu. Ilyashenko, eds.), NATO Science Series II Math. Phys. Chem., (2004), vol.137, pp. 267-294. Kluwer Academic Publishers, Dordrecht.

Papers in preparation

1. (with Yu.S.Ilyashenko) An estimate of the number of zeroes of abelian integral corresponding to special hamiltonian of arbitrary degree. A preliminary version is available at http://xxx.lanl.gov/abs/math.DS/0112156.
2. Instability of free nondiscrete subgroups in Lie groups. - Submitted to "Transformation Groups" journal. http:/xxx.lanl.gov/abs/math.DS/0409556
3. On convergence of generalized continued fractions and a Ramanujan's conjecture. - Submitted to Comptes-Rendus de l'Academie de Sciences, Paris, S\'er. 1 Math. http://xxx.lanl.gov/abs/math.DS/0412438