Edit Profile (opens in new tab) Kurakin, Leonid Gennadievich Compute Distance To: Compute Author ID: kurakin.leonid-g Published as: Kurakin, L. G.; Kurakin, Leonid G.; Kurakin, Leonid more...less Further Spellings: Куракин Леонид Геннадиевич External Links: Math-Net.Ru · dblp Documents Indexed: 37 Publications since 1986 Co-Authors: 7 Co-Authors with 25 Joint Publications 117 Co-Co-Authors all top 5 Co-Authors 12 single-authored 13 Yudovich, Viktor Iosifovich 8 Ostrovskaya, Irina V. 2 Kurdoglyan, Aik V. 2 Lysenko, Irina A. 2 Sokolovskiy, Mikhail A. 1 Borisov, Alekseĭ Vladimirovich 1 Melekhov, Andrey all top 5 Serials 7 Chaos 7 Regular and Chaotic Dynamics 3 Mathematical Notes 3 Russian Journal of Nonlinear Dynamics 2 Journal of Applied Mathematics and Mechanics 2 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Siberian Mathematical Journal 1 Izvestiya Severo-Kavkazskogo Nauchnogo Tsentra Vyssheĭ Shkoly. Estestvennye Nauki 1 Journal of Nonlinear Science 1 Russian Academy of Sciences. Doklady. Mathematics 1 Physics-Doklady 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Severo-Kavkazskiĭ Region. Estestvennye Nauki 1 Doklady Mathematics 1 Journal of Mathematical Fluid Mechanics 1 Doklady Physics 1 Differential Equations 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Proceedings of the Steklov Institute of Mathematics all top 5 Fields 20 Ordinary differential equations (34-XX) 17 Fluid mechanics (76-XX) 15 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of particles and systems (70-XX) 1 Operator theory (47-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 30 Publications have been cited 164 times in 60 Documents Cited by ▼ Year ▼ The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520Kurakin, L. G.; Yudovich, V. I. 43 2002 On nonlinear stability of the regular vortex systems on a sphere. Zbl 1080.76031Kurakin, L. G. 15 2004 Nonlinear stability analysis of a regular vortex pentagon outside a circle. Zbl 1252.76017Kurakin, Leonid G.; Ostrovskaya, Irina V. 9 2012 Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. Zbl 1211.76027Kurakin, L. G.; Ostrovskaya, I. V. 8 2010 On stability of thomson’s vortex \(N\)-gon in the geostrophic model of the point Bessel vortices. Zbl 1401.76037Kurakin, Leonid G.; Ostrovskaya, Irina V. 8 2017 On the stability of discrete tripole, quadrupole, Thomson’ vortex triangle and square in a two-layer/homogeneous rotating fluid. Zbl 1346.76204Kurakin, Leonid G.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A. 8 2016 Bifurcation of the branching of a cycle in \(n\)-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043Kurakin, L. G.; Yudovich, V. I. 7 1997 On the stability of the regular \(n\)-sided polygon of vortices. Zbl 0832.76028Kurakin, L. G. 7 1994 On stability of a regular vortex polygon in the circular domain. Zbl 1097.76031Kurakin, Leonid 7 2005 The stability of the steady rotation of a system of three equidistant vortices outside a circle. Zbl 1272.76116Kurakin, L. G. 7 2011 A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. Zbl 1348.76041Kurakin, Leonid; Melekhov, Andrey; Ostrovskaya, Irina 7 2016 On the stability of Thomson’s vortex configurations inside a circular domain. Zbl 1229.37055Kurakin, L. G. 6 2010 Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031Kurakin, L. G.; Yudovich, V. I. 4 2000 On stability of the Thomson’s vortex \(N\)-gon in the geostrophic model of the point vortices in two-layer fluid. Zbl 1423.76076Kurakin, Leonid G.; Lysenko, Irina A.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A. 4 2019 Influence of annular boundaries on Thomson’s vortex polygon stability. Zbl 1345.70034Kurakin, L. G. 4 2014 On the stability of Thomson’s vortex pentagon inside a circular domain. Zbl 1270.76018Kurakin, Leonid G. 3 2012 Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry. Zbl 0953.34043Kurakin, L. G. 2 1998 Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028Kurakin, L. G.; Yudovich, V. I. 2 1986 On the stability of Thomson’s vortex \(N\)-gon and a vortex tripole/quadrupole in geostrophic models of Bessel vortices and in a two-layer rotating fluid: a review. Zbl 1446.76114Kurakin, Leonid G.; Ostrovskaya, Irina V. 2 2019 On the stability of a system of two identical point vortices and a cylinder. Zbl 1459.76055Borisov, A. V.; Kurakin, L. G. 1 2020 Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry. Zbl 1020.37029Kurakin, L. G.; Yudovich, V. I. 1 2000 Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025Kurakin, L. G.; Yudovich, V. I. 1 2000 Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521Kurakin, L. G.; Yudovich, V. I. 1 2000 On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040Kurakin, L. G.; Yudovich, V. I. 1 2004 Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566Kurakin, L. G.; Yudovich, V. I. 1 2001 On the Lyapunov chain of stability criteria in the critical case of a Jordan 2-block. Zbl 0854.34052Kurakin, L. G. 1 1994 Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067Kurakin, L. G.; Yudovich, V. I. 1 2003 On the stability criteria in A. M. Lyapunov’s paper “A study of one of the special cases of the problem of stability of motion”. Zbl 1324.34109Kurakin, L. G. 1 2009 Semi-invariant form of equilibrium stability criteria for systems with one cosymmetry. Zbl 1445.34086Kurakin, Leonid G.; Kurdoglyan, Aik V. 1 2019 On the stability of the orbit and the invariant set of Thomson’s vortex polygon in a two-fluid plasma. Zbl 1453.82085Kurakin, L. G.; Lysenko, I. A. 1 2020 On the stability of a system of two identical point vortices and a cylinder. Zbl 1459.76055Borisov, A. V.; Kurakin, L. G. 1 2020 On the stability of the orbit and the invariant set of Thomson’s vortex polygon in a two-fluid plasma. Zbl 1453.82085Kurakin, L. G.; Lysenko, I. A. 1 2020 On stability of the Thomson’s vortex \(N\)-gon in the geostrophic model of the point vortices in two-layer fluid. Zbl 1423.76076Kurakin, Leonid G.; Lysenko, Irina A.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A. 4 2019 On the stability of Thomson’s vortex \(N\)-gon and a vortex tripole/quadrupole in geostrophic models of Bessel vortices and in a two-layer rotating fluid: a review. Zbl 1446.76114Kurakin, Leonid G.; Ostrovskaya, Irina V. 2 2019 Semi-invariant form of equilibrium stability criteria for systems with one cosymmetry. Zbl 1445.34086Kurakin, Leonid G.; Kurdoglyan, Aik V. 1 2019 On stability of thomson’s vortex \(N\)-gon in the geostrophic model of the point Bessel vortices. Zbl 1401.76037Kurakin, Leonid G.; Ostrovskaya, Irina V. 8 2017 On the stability of discrete tripole, quadrupole, Thomson’ vortex triangle and square in a two-layer/homogeneous rotating fluid. Zbl 1346.76204Kurakin, Leonid G.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A. 8 2016 A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. Zbl 1348.76041Kurakin, Leonid; Melekhov, Andrey; Ostrovskaya, Irina 7 2016 Influence of annular boundaries on Thomson’s vortex polygon stability. Zbl 1345.70034Kurakin, L. G. 4 2014 Nonlinear stability analysis of a regular vortex pentagon outside a circle. Zbl 1252.76017Kurakin, Leonid G.; Ostrovskaya, Irina V. 9 2012 On the stability of Thomson’s vortex pentagon inside a circular domain. Zbl 1270.76018Kurakin, Leonid G. 3 2012 The stability of the steady rotation of a system of three equidistant vortices outside a circle. Zbl 1272.76116Kurakin, L. G. 7 2011 Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. Zbl 1211.76027Kurakin, L. G.; Ostrovskaya, I. V. 8 2010 On the stability of Thomson’s vortex configurations inside a circular domain. Zbl 1229.37055Kurakin, L. G. 6 2010 On the stability criteria in A. M. Lyapunov’s paper “A study of one of the special cases of the problem of stability of motion”. Zbl 1324.34109Kurakin, L. G. 1 2009 On stability of a regular vortex polygon in the circular domain. Zbl 1097.76031Kurakin, Leonid 7 2005 On nonlinear stability of the regular vortex systems on a sphere. Zbl 1080.76031Kurakin, L. G. 15 2004 On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040Kurakin, L. G.; Yudovich, V. I. 1 2004 Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067Kurakin, L. G.; Yudovich, V. I. 1 2003 The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520Kurakin, L. G.; Yudovich, V. I. 43 2002 Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566Kurakin, L. G.; Yudovich, V. I. 1 2001 Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031Kurakin, L. G.; Yudovich, V. I. 4 2000 Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry. Zbl 1020.37029Kurakin, L. G.; Yudovich, V. I. 1 2000 Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025Kurakin, L. G.; Yudovich, V. I. 1 2000 Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521Kurakin, L. G.; Yudovich, V. I. 1 2000 Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry. Zbl 0953.34043Kurakin, L. G. 2 1998 Bifurcation of the branching of a cycle in \(n\)-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043Kurakin, L. G.; Yudovich, V. I. 7 1997 On the stability of the regular \(n\)-sided polygon of vortices. Zbl 0832.76028Kurakin, L. G. 7 1994 On the Lyapunov chain of stability criteria in the critical case of a Jordan 2-block. Zbl 0854.34052Kurakin, L. G. 1 1994 Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028Kurakin, L. G.; Yudovich, V. I. 2 1986 all cited Publications top 5 cited Publications all top 5 Cited by 58 Authors 22 Kurakin, Leonid Gennadievich 8 Ostrovskaya, Irina V. 6 Yudovich, Viktor Iosifovich 3 Newton, Paul K. 3 Reinaud, Jean N. 2 Boatto, Stefanella 2 Borisov, Alekseĭ Vladimirovich 2 Cabral, Hildeberto Eulalio 2 Cao, Daomin 2 Carvalho, Adecarlos C. 2 Govorukhin, Vasily N. 2 Kim, Sun-Chul 2 Kizner, Ziv 2 Koiller, Jair 2 Kurdoglyan, Aik V. 2 Lysenko, Irina A. 2 Qin, Guolin 2 Sakajo, Takashi 2 Sokolovskiy, Mikhail A. 2 Zhan, Weicheng 2 Zou, Changjun 1 Artemova, Elizaveta Markovna 1 Banica, Valeria 1 Bizyaev, Ivan Alekseevich 1 Dritschel, David Gerard 1 Frischmuth, Kurt 1 García-Azpeitia, Carlos 1 García-Naranjo, Luis C. 1 Garcia, Claudia I. 1 Gebhard, Björn 1 Jamaloodeen, Mohamed I. 1 Koshel, Konstantin V. 1 Kovaleva, Ekaterina S. 1 Makarenko, Nikolay I. 1 Makarov, V. G. 1 Makridin, Zakhar V. 1 Mamaev, Ivan Sergeevich 1 Melekhov, Andrey 1 Miot, Evelyne 1 Naumov, Igor V. 1 Okulov, Valery L. 1 Ortega, Rafael 1 Ostrovskyi, Vitalii 1 Ramodanov, Sergey M. 1 Ryzhov, Eugene A. 1 Shevchenko, Igor V. 1 Shnol’, Èmmanuil Èl’evich 1 Shokraneh, Houman 1 Simó, Carles 1 Sohn, Sung-Ik 1 Sokolov, Sergeĭ Viktorovich 1 Sørensen, Jens Nørkær 1 Tsibulin, B. G. 1 Tsibulin, V. G. 1 Tsybulin, Vyacheslav G. 1 Vetchanin, Evgeniĭ Vladimirovich 1 Yagasaki, Kazuyuki 1 Yim, Habin all top 5 Cited in 23 Serials 18 Regular and Chaotic Dynamics 6 Chaos 5 Journal of Nonlinear Science 3 Physica D 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Russian Journal of Nonlinear Dynamics 2 Fluid Dynamics 2 Journal of Fluid Mechanics 2 Physics of Fluids 2 Proceedings of the Steklov Institute of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Mathematical Notes 1 Prikladnaya Matematika i Mekhanika 1 Journal of Functional Analysis 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Journal of Applied Mechanics and Technical Physics 1 Doklady Physics 1 Differential Equations 1 Nonlinear Analysis. Real World Applications 1 Journal of Geometric Mechanics all top 5 Cited in 12 Fields 45 Fluid mechanics (76-XX) 17 Dynamical systems and ergodic theory (37-XX) 14 Ordinary differential equations (34-XX) 12 Mechanics of particles and systems (70-XX) 4 Partial differential equations (35-XX) 2 History and biography (01-XX) 2 Geophysics (86-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year