Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Phone: +7 (495) 772 95 90 * 15164, +33 4 72 72 84 20
E-mail: Website: https://www.umpa.ens-lyon.fr/umpa/annuaire/glutsyuk-alexey Keywords: 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.
UDC: 517.9, 517.5
MSC: 58F23, 57M50
Subject:
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
