Dynamical systems, real and complex billiards, integrable billiards, periodic orbits, ordinary differential equations in real and complex time, holomorphic foliations, Stokes phenomena, model of Josephson junction in superconductivity
Dynamical systems, real and complex billiards, analytic theory of ordinary differential equations in real and complex time, foliations, complex geometry and dynamics, transformation groups.
Main publications:
A.A.Glutsyuk, “On polynomially integrable Birkhoff billiards on surfaces of constant curvature”, Klassifikatsiya polinomialno integriruemykh ploskikh bilyardov: reshenie polinomialnoi versii gipotezy Birkhgofa, sformulirovannoi S.V.Bolotinym, J. Eur. Math. Society, 23:3 (2021), 994–1049
A.A.Glutsyuk, “On 4-reflective complex analytic planar billiards”, Vvedenie kompleksnykh bilyardov na dvumernoi kompleksnoi ploskosti. Klassifikatsiya kompleksnykh bilyardov s otkrytym mnozhestvom 4-periodicheskikh orbit. Primenenie k veschestvennym bilyardam, vklyuchaya reshenie dvumernoi gipotezy Tabachnikova o kommutiruyuschikh bilyardakh, J. Geom Analysis, 27:1 (2017), 183–238
A. Glutsyuk, “Instability of nondiscrete free subgroups in Lie groups”, Dokazano, chto vsyakuyu konechno-porozhdennuyu nediskretnuyu svobodnuyu podgruppu v proizvolnoi gruppe Li mozhno prevratit v nesvobodnuyu podgruppu skol ugodno malym vozmuscheniem obrazuyuschikh, Transformations groups, 16:2 (2011), 413–479
Yu. Bibilo; A. Glutsyuk, “On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation”, Preprint, 72 str, podan v pechat. Issledovano semeistvo differentsialnykh uravnenii na dvumernom tore, modeliruyuschee silno shuntirovannyi perekhod Dzhozefsona v sverkhprovodimosti. Resheny dve gipotezy o peremychkakh zon fazovogo zakhvata (o raspolozhenii na odnoi pryamoi i o polozhitelnosti) s pomoschyu novykh razrabotannykh metodakh, ispolzuyuschikh teoriyu kompleksnykh lineinykh uravnenii (yavlenie Stoksa i izomonodromnye deformatsii, opisyvaemye uravneniyami Penleve 3) i teoriyu bystro-medlennykh sistem, Preprint series arxiv.org (Working papers of Cornell University), 2020, https://arxiv.org/abs/2011.07839
A. A. Glutsyuk, I. V. Izmestiev, S. L. Tabachnikov, “Four equivalent properties of integrable billiards”, Israel Journal of Mathematics, 241 (2021), 693–719 , arXiv: 1909.09028
3.
Yu. P. Bibilo, A. A. Glutsyuk, “On families of constrictions in the model of an overdamped Josephson junction”, Russian Math. Surveys, 76:2 (2021), 360–362
2020
4.
A.A.Glutsyuk, “On commuting billiards in higher-dimensional spaces of constant curvature”, Pacific J. Math., 305:2 (2020), 577–595 , arXiv: 1807.10567
5.
A.A.Glutsyuk, I. V. Netay, “On spectral curves and complexified boundaries of phase-lock areas in a model of Josephson junction”, J. Dyn. Control Systems, 26 (2020), 785–820 , arXiv: https://arxiv.org/abs/1908.08491 (cited: 1) ;
6.
A. V. Borisov, I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The conference “Dynamics in Siberia”, Novosibirsk, February 24–29, 2020”, Sib. elektron. matem. izv., 17 (2020), 68–96
2019
7.
A. A. Glutsyuk, “On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation”, J. Dyn. Control Systems, 25:3 (2019), 323–349 , arXiv: 1805.02624 (cited: 2) (cited: 3);
8.
V. M. Buchstaber, A. A. Glutsyuk, “Total positivity, Grassmannian and modified Bessel functions”, Functional Analysis and Geometry: Selim Grigorievich Krein Centennial, Contemp. Math., 733, AMS, 2019, 97–107 (cited: 1) (cited: 1); ;
9.
E. Bakaev, A. Glutsyuk, S. Dorichenko, A. Zaslavskii, P. Kozhevnikov, L. Mednikov, V. Novikov, V. Retinskii, A. Ryabichev, E. Rjabov, A. Semenov, M. Skopenkov, I. Frolov, A. Shapovalov, Kvant, 2019, no. 12, 34–35
10.
A. Bufetov, A. Glutsyuk, N. Goncharuk, S. Gusein-Zade, Yu. Kudryashov, S. Lando, A. Sosinskii, V. Timorin, M. Tsfasman, “Yuliyu Sergeevichu Ilyashenko — 75”, Mosc. Math. J., 19:2 (2019), 185–188
11.
I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The Conference “Dynamics in Siberia”, Novosibirsk, February 25 – March 2, 2019”, Sib. elektron. matem. izv., 16 (2019), 16–39
A. A. Glutsyuk, “On two-dimensional polynomially integrable billiards on surfaces of constant curvature”, Doklady Mathematics, 98:1 (2018), 382–385 (cited: 6) (cited: 4)
14.
A. A. Glutsyuk, S. Ramassamy, “A first integrability result for Miquel dynamics”, J. Geom. and Physics, 130 (2018), 121–129 , arXiv: 1801.01082 (cited: 1) (cited: 1);
15.
I. A. Dynnikov, A. A. Glutsyuk, G. N. Kulipanov, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The Conference «Dynamics in Siberia» dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, February 26–March 4, 2018”, Sib. elektron. matem. izv., 15 (2018), 10–38
2017
16.
A. A. Glutsyuk, L. G. Rybnikov, “On families of differential equations on two-torus with all phase-lock areas”, Nonlinearity, 30 (2017), 61–72 , arXiv: 1505.06975 (cited: 2) (cited: 3)
17.
A. A. Glutsyuk, “On 4-reflective complex analytic planar billiards”, J. Geom Analysis, 27:1 (2017), 183–238 , arXiv: 1405.5990 (cited: 4) (cited: 4)
18.
V. M. Buchstaber, A. A. Glutsyuk, “On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect”, Proc. Steklov Inst. Math., 297 (2017), 50–89 (cited: 6) (cited: 7);
19.
I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The conference “Dynamics in Siberia”, Novosibirsk, February 26–March 4, 2017”, Sib. elektron. matem. izv., 14 (2017), 7–30
2016
20.
V. M. Buchstaber, A A Glutsyuk, “On determinants of modified Bessel functions and entire solutions of double confluent Heun equations”, Nonlinearity, 29 (2016), 3857–3870 , arXiv: 1509.01725 (cited: 8) (cited: 8);
2014
21.
A. A. Glutsyuk, “On odd-periodic orbits in complex planar billiards”, J. Dyn. Control Systems, 20:3 (2014), 293–306
22.
A. A. Glutsyuk, V. A. Kleptsyn, D. A. Filimonov, I. V. Shchurov, “On the Adjacency Quantization in an Equation Modeling the Josephson Effect”, Funct. Anal. Appl., 48:4 (2014), 272–285 (cited: 10) (cited: 10)
A. I. Bufetov, A. A. Glutsyuk, S. M. Gusein-Zade, A. S. Gorodetski, V. Yu. Kaloshin, A. G. Khovanskii, V. A. Kleptsyn, S. Yu. Nemirovskii, A. B. Sossinsky, M. A. Tsfasman, V. A. Vassiliev, S. Yu. Yakovenko, “Yulij Sergeevich Ilyashenko”, Mosc. Math. J., 14:2 (2014), 173–179
2012
25.
A. A. Glutsyuk, Yu. G. Kudryashov, “No planar billiard possesses an open set of quadrilateral trajectories”, Journal of Modern Dynamics, 6:3 (2012), 287–326
2011
26.
A. A. Glutsyuk, Yu. G. Kudryashov, “On quadrilateral orbits in planar billiards”, Doklady Mathematics, 83:3 (2011), 371–373
27.
A. A. Glutsyuk, “Instability of nondiscrete free subgroups in Lie groups”, Transformations groups, 16:2 (2011), 413–479 , arXiv: math/0409556v4
2010
28.
A. A. Glutsyuk, C. Sabot, “Stokes matrices of hypergeometric integrals”, Annales de l'Institut Fourier, 60:1 (2010), 291–317 , arXiv: 0712.1707
29.
A. Glutsyuk, “On density of horospheres in dynamical laminations”, Mosc. Math. J., 10:3 (2010), 547–591 (cited: 1) ;
30.
A. A. Glutsyuk, “Unique ergodicity of horospheric foliations revisited”, Journal of fixed point theory and its applications, 8, The Steve Smale Festschrift:1 (2010), 113–149
2007
31.
A. A. Glutsyuk, Yu. S. Ilyashenko, “Restricted version of the infinitesimal Hilbert 16th problem”, Mosc. Math. J., 7:2 (2007), 281–325 (cited: 4) (cited: 4);
2006
32.
A. A. Glutsyuk; Yu. S. Ilyashenko, “Restricted infinitesimal Hilbert sixteenths problem”, Doklady Mathematics, 73:2 (2006), 185–189
33.
A. A. Glutsyuk, “An explicit formula for period determinant”, Ann. Inst. Fourier, 56:4 (2006), 887–917
2005
34.
A. A. Glutsyuk, “Upper bounds of topology of complex polynomials in two variables”, Mosc. Math. J., 5:4 (2005), 781–828 (cited: 3) (cited: 3);
35.
A. A. Glutsyuk, “On the monodromy group of confluent linear equations”, Mosc. Math. J., 5:1 (2005), 67–90 (cited: 1) (cited: 2); ;
36.
A. A. Glutsyuk, “On convergence of generalized continued fractions and Ramanujan conjecture”, C. R. Math. Acad. Sci. Paris, 341:7 (2005), 427–432 , arXiv: math/0412445
37.
D. V. Anosov, V. I. Arnol'd, A. A. Glutsyuk, A. S. Gorodetski, V. Y. Kaloshin, A. B. Katok, A. G. Khovanskii, S. K. Lando, A. B. Sossinski, M. A. Tsfasman, S. Yu. Yakovenko, “Yulij S. Ilyashenko”, Mosc. Math. J., 5:1 (2005), 3–4
2004
38.
A. A. Glutsyuk, “Simultaneous metric uniformization of foliations by Riemann surfaces”, Commentarii Mathematici Helvetici, 79:4 (2004), 704–752
39.
A. A. Glutsyuk, “Resonant confluence of singular points and Stokes phenomena”, Journal of Dynamical and Control Systems, 10:2 (2004), 253–302
2002
40.
A. A. Glutsyuk, “On simultaneous uniformization and local nonuniformizability”, C.R. Acad. Sci. Paris, Série 1 Math., 334 (2002), 489–494
2001
41.
A. A. Glutsyuk, “Nonuniformizable skew cylinders: a counterexample to the simultaneous uniformization problem”, C.R. Acad. Sci. Paris, Série 1 Math., 332 (2001), 209–214 , arXiv: math/0001047
42.
A. A. Glutsyuk, “Confluence of singular points and the nonlinear Stokes Phenomena”, Transactions of Moscow Mathematical Society, 62 (2001), 49–95
2000
43.
A. A. Glutsyuk, “On the codimension of the set of one-dimensional polynomial foliations on $\mathbb{C}^ n$ and $\mathbb{CP}^n$ that do not satisfy a sufficient condition for the hyperbolicity of leaves”, St. Petersburg Math. J., 11:4 (2000), 567–587
1999
44.
A. A. Glutsuk, “Stokes operators via limit monodromy of generic perturbation”, Journal of Dynamical and Control Systems, 5:1 (1999), 101–135 https://link.springer.com/article/10.1023/A:1021744801409
1998
45.
A. A. Glutsyuk, “Limit sets at infinity for liftings of non-self-intersecting curves on the torus to the plane”, Math. Notes, 64:5 (1998), 579–589
1996
46.
A. A. Glutsyuk, “Hyperbolicity of the leaves of a generic one-dimensional holomorphic foliation on a nonsingular projective algebraic variety”, Proc. Steklov Inst. Math., 213 (1996), 83–103
1995
47.
A. A. Glutsyuk, “Asymptotic Stability of Linearizations of a Planar Vector Field with a Singular Point Implies Global Stability”, Funct. Anal. Appl., 29:4 (1995), 238–247 (cited: 7)
1994
48.
A. A. Glutsyuk, “The Hyperbolicity of Phase Curves of a Generic Polynomial Vector Field in $\mathbb{C}^n$”, Funct. Anal. Appl., 28:2 (1994), 77–84 (cited: 1)
49.
A. A. Glutsyuk, “A complete solution of the Jacobian problem for vector fields on the plane”, Russian Math. Surveys, 49:3 (1994), 185–186 (cited: 22)
1993
50.
A. A. Glutsyuk, “An analogue of Cayley's theorem for cyclic symmetric connected graphs with one cycle connected with generalized Lyashko–Looijenga covers”, Russian Math. Surveys, 48:2 (1993), 182–183
51.
A. A. Glutsyuk, “An analogue of Cayley's theorem for cyclically symmetric connected graphs with a single cycle that are associated with generalized Lyashko–Looijenga covers”, Russian Math. Surveys, 48:4 (1993), 247–248
О квантовании перемычек в уравнениях Джозефсона A. A. Glutsyuk Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS March 21, 2012 18:30
2021
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