Alexey Glutsyuk

Liste de publications: journaux, actes de colloques et preprints.

A. Billards réels et complexes: intégrabilité et les orbites périodiques.

 A1. Intégrabilité et caustiques.

53. On rationally integrable planar dual multibilliards and piecewise smooth projective billiards.-- 78 pages. Preprint (pdf)

52. On rationally integrable planar projective billiards -- 98 pages. Soumis.  Preprint https://arxiv.org/abs/2112.07056 (pdf)

51. On polynomially integrable Birkhoff billiards on surfaces of constant curvature --  Journal of the European Mathematical Society (JEMS), 23 (2021), Issue 3,  994--1049. (pdf)

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

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

48. On infinitely many foliations by caustics in strictly convex non-closed billiards. - 61 pages. Preprint https://arxiv.org/pdf/2104.01362 (pdf)


A2. Orbites périodiques.

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

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

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

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

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

42. On commuting billiards in higher-dimensional spaces of constant curvature. Pacific Journal of Mathematics, 305 (2020), No. 2, 577--595. (pdf)


A3. Courbes convexes sur des surfaces Riemanniennes avec propriétés remarquables liées aux billards intégrables

41. (avec Ivan Izmestiev and Sergei Tabachnikov). Four equivalent properties of integrable billiards. - Israel Journal of Mathematics, 241 (2021), 693--719. (pdf)

40. On curves with Poritsky property. - 75 pages.   A paraitre dans le Journal of Fixed Point Theory and Applications, tome spécial dedié au 60-ème anniversaire de Prof. Claude Viterbo.  (pdf)


A4. Compositions des reflections des billards: leur densité

39. Density of thin film billiard reflection pseudogroup in Hamiltonian symplectomorphism pseudogroup. - 45 pages.  A paraitre dans Israel Journal of Mathematics. (pdf)


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

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

 C. Sous groupes non libres dans les groupes de Lie

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

 

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

36. (avec Yu.P.Bibilo). On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation. -- Nonlinearity 35 (2022), 5427--5480.(pdf)

35.  Version abrégée de l'article mentionné ci-dessus: Russian Mathematical Surveys, 76:2 (2021), 360--362.

34. 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, 25:3 (2019), 323--349. (pdf)

33. (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)

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

31. (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)

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

29.  (avec Victor Buchstaber) Total positivity, Grassmannian and modified Bessel functions. -- Functional Analysis and Geometry: Selim Grigorievich Krein Centennial, Contemp. Math., 733, AMS, 2019, 97–107. (pdf)

28.  (avec Igor Netay) On spectral curves and complexified phase-lock areas in a model of Josephson junction.  -- Journal of Dynamical and Control Systems,   26
(2020), 785--820. (pdf)


E. Feuilletages par surfaces de Riemann et uniformisation

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

26. 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.

25. 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.

24. 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)

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

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

21. (Actes de colloque)  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)

F. Laminations horosphériques en la dynamique rationnelle


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

19. (Actes de colloque)  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.

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

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


G. Confluence des points singuliers et le phénomène de Stokes

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

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

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

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

12. (Actes de colloque) 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.

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


H. Abelian integrals and quantitative algebraic geometry

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

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

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

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


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

6. 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).

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

4.  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).



J. Convergence des fractions continues généralisées et une conjecture de Ramanujan

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


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

2. 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.

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

1. 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.