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Alexey Glutsyuk

Chargé de recherches au CNRS

Unité de Mathématiques Pures et Appliquées, M.R. (UMPA, UMR 5669 CNRS),
Ecole Normale Supérieure de Lyon,
46, allée d'Italie, 
69364 Lyon Cedex 07, FRANCE

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Contact

E-mail: aglutsyu   (at)  ens-lyon.fr
Bureau: Sud 431
Tél: (+33) 4-72-72-84-20
Fax: (+33) 4-72-72-84-80

Un court CV

Thèmes de recherche: 

  Systèmes dynamiques réels et complexes: billards,
la théorie analytique des équations différentielles ordinaires, feuilletages holomorphes,
groupes de transformations, modèle de l'effet de  Josephson dans la supraconductivité

Habilitation (2008). (pdf)

Articles

Billards réels et complexes: intégrabilité et les orbites périodiques

 - On polynomially integrable Birkhoff billiards on surfaces of constant curvature -- A paraitre dans le Journal of the European Mathematical Society (JEMS).  69 pages. Disponible sur https://arxiv.org/abs/1706.04030 (pdf)

 - On two-dimensional polynomially integrable billiards on surfaces of constant curvature. -- Doklady Mathematics, 98 (2018) No. 1, 382--385. (pdf)

- (avec Eugeny Shustin) On polynomially integrable planar outer billiards and curves with symmetry property -- Mathematische Annalen, 372 (2018), 1481--1501. (pdf)

- On 4-reflective complex analytic planar billiards. -- Journal of Geometric Analysis, 27 (2017), no. 1, 183--238. (pdf)

- On quadrilateral orbits in complex algebraic planar billiards. -- Moscow Mathematical Journal 14 (2014), No. 2, 239--289. (pdf)

- On odd-periodic orbits in complex planar billiards. - Journal of Dynamical and Control Systems, 20 (2014), No. 3, 293--306. (pdf)

- (avec Yury Kudryashov). No planar billiard possesses an open set of quadrilateral trajectories, - Journal of Modern Dynamics, 6 (2012), no. 3, 287--326.

- (avec Yury Kudryashov). On quadrilateral orbits in planar billiards, -- Doklady Mathematics, 83, 371--373 (2011).

- On commuting billiards in higher dimensions. Soumis pour publication. Preprint https://arxiv.org/abs/1807.10567 (pdf)

 Courbes avec la propriété de Poritsky

- On curves with Poritsky property. 53 pages. Preprint https://arxiv.org/abs/1901.01881    (Lien vers la version arxiv) (pdf)

 La dynamique de Miquel sur les agencements de cercles: un premier résultat d'intégrabilité

- (avec Sanjay Ramassamy) A first integrability result for Miquel dynamics. -- Journal of Geometry and Physics, 130 (2018), 121--129. (pdf)

 Sous groupes non libres dans les groupes de Lie

- Instability of nondiscrete free subgroups in Lie groups. - Transformations groups, 16 (2011), no. 2, 413--479. (pdf)

  Modèle de l'effet de Josephson dans la supra-conductivité

- On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation. -- Journal of Dynamical and Control Systems. Published "Online First": https://doi.org/10.1007/s10883-018-9411-1   29 pages. (pdf)

- (avec Dmitry Filimonov, Victor Kleptsyn, Ilya Schurov). On the adjacency quantization in an equation modelling the Josephson effect. - Functional Analysis and its Applications, 48 (2014), 272--285.(pdf téléchargeable)

- (avec Victor Buchstaber) On determinants of modified Bessel functions and entire solutions of double confluent Heun equations. -- Nonlinearity 29 (2016), 3857--3870. (pdf)

- (avec Victor Buchstaber) On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect. -- Proceeding of Steklov Institute of Mathematics, 297 (2017), 50--89. (pdf)

- (avec Leonid Rybnikov) On families of differential equations on two-torus with all phase-lock areas. -- Nonlinearity, 30 (2017), 61--72. (pdf)

- (avec Victor Buchstaber) Total positivity, Grassmannian and modified Bessel functions. -- To appear in the special volume of the AMS series "Contemporary Mathematics" dedicated to the centennial of Professor Selim Grigorievich Krein. (pdf)


Feuilletages par surfaces de Riemann et uniformisation

- The hyperbolicity of phase curves of a generic polynomial vector field in Cn. - Functional analysis and its Applications, 28 (1994), No. 2, 77-84.

- Hyperbolicity of leaves of a generic one-dimensional holomorphic foliation on
a nonsingular projective algebraic manifold - Proceedings of Steklov Mathematical Institute, 213 (1996), No.2, 83-103.

- On the codimension of the set of one-dimensional polynomial foliations on Cn and CPn that do not satisfy the sufficient conditions for hyperbolicity of leaves. - Saint-Petersburg Mathematical Journal, 11 (2000), No 4, 567-587.

- Nonuniformizable skew cylinders. A counterexample to the simultaneous uniformization problem. - Comptes Rendus de l'Académie des Sciences, Paris,  Série 1  Mathématiques, vol. 332, issue 3, pp. 209-214. (pdf)

- On simultaneous uniformization and local non-uniformizability. - Comptes-Rendus de l'Académie des Sciences, Paris, Série 1 Mathématiques, t.334 (2002), p.489-494.

- Simultaneous metric uniformization of foliations by Riemann surfaces" Commentarii Mathematici Helvetici, vol. 79, Issue 4 (2004), pp.704-752.

- Simple proofs of uniformization theorems. - In Fields Inst. Commun., 53 (2008), 125{143. Holomorphic dynamics and renormalization: a volume in honour of John Milnor's 75th birthday. (pdf)


Laminations horosphériques en la dynamique rationnelle


- On density of horospheres in dynamical laminations. - Moscow Math. Journal, Vol. 10 (2010), no. 3, p. 547-591. (pdf)

- A survey on minimality of horospheric laminations associated to rational functions. - In Fields Institute Communications 51 (2007), 269-287. Proceedings of the Partially hyperbolic dynamics, laminations, and Teichmuller flow Workshop, January 5-9, 2006.

- Unique ergodicity of horospheric foliations revisited. - Journal of fixed point theory and its applications, 8 (2010), no. 1 (The Steve Smale Festschrift), 113-149.

- Affine and hyperbolic laminations in holomorphic dynamics. - Panoramas and Syntheses, 34 (2011), 149-202.


Confluence des points singuliers et le phénomène de Stokes

- Stokes operators via limit monodromy of a generic deformation. - Journal of Dynamical and Control Systems, v.5 (1999) No 1, 101-135.

- Confluence of singular points and the nonlinear Stokes Phenomena  - Transactions of Moscow Mathematical Society, 2001, 49-95.

- Resonant confluence of singular points and Stokes phenomena. - Journal of Dynamical and Control Systems, vol. 10 (2004), No. 2 (April),  253--302.

- On the monodromy group of confluenting linear equations. - Moscow Math. J., 5 (2005), no. 1, 67-90. (pdf)

- 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.

- (avec C.Sabot). Stokes matrices of hypergeometric integrals. - Annales de l'Institut Fourier, 60 (2010), no. 1, p. 291--317. (pdf)


Abelian integrals and quantitative algebraic geometry

- (avec Yu.S.Ilyashenko). Restricted version of the infinitesimal Hilbert 16-th problem. - Moscow Math. J. 7 (2007), no. 2, 281-325.(pdf)

- (avec Yu.S.Ilyashenko). Restricted infinitesimal Hilbert sixteenths problem. -
Doklady Mathematics, 73 (2006), No 2, 185-189.

- Upper bounds of topology of complex polynomials in two variables. - Mosc. Math. J. 5 (2005), no. 4, 781--828. (pdf).

- An explicit formula for period determinant. - Ann. Inst. Fourier (Grenoble) 56 (2006), no. 4, 887--917.  (pdf).


Stabilité des champs de vecteurs: solution du problème de Markus--Yamabe

- Asymptotic stability of linearizations of planar vector field with a singular point implies global stability -
Functional Analysis and its Applications 29 (1995), No. 4,  238-247 (1996).

- Complete solution of the Jacobian problem for planar vector fields -
Russian Math. Surveys 49 (1994), no. 3, 185--186.

- Asymptotic stability of linearizations of a vector field in R3 with a singular point does not imply global stability. -- Preprint présenté pour publication dans Communicaciones del CIMAT, Guanajuato, Mexico, par X.Gomez-Mont en 1996. 18 pages (pdf).



-Convergence des fractions continues généralisées et une conjecture de Ramanujan

- On convergence of generalized continued fractions and Ramanujan conjecture. - Comptes Rendus Mathématiques de l'Académie dse Sciences. Paris 341 (2005), no. 7, 427--432.


- Relevements au plan des courbes sans auto-intersections sur le tore

- Limit sets at infinity of liftings to the plane of nonself-intersected curves in the torus - Mathematical Notes, 64 (1998), No 5-6, 579-589.

-La théorie de singularités: revetements de Lyashko--Looijenga.

- The analogue of Cayley's theorem for the cyclically-symmetric connected graphs with a single cycle that are related to the generalized Lyashko --  Looijenga coverings. -- Russian Mathematicals Surveys 48 (1993), No. 2, 182-183.