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 Author ID: kurakin.leonid-g Published as: Kurakin, L. G.; Kurakin, Leonid G.; Kurakin, Leonid 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
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### 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
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### Serials

 7 Chaos 7 Regular and Chaotic Dynamics 3 Mathematical Notes 3 Nelineĭnaya Dinamika 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
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### 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)

### Citations contained in zbMATH Open

30 Publications have been cited 146 times in 57 Documents Cited by Year
The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520
Kurakin, L. G.; Yudovich, V. I.
2002
On nonlinear stability of the regular vortex systems on a sphere. Zbl 1080.76031
Kurakin, L. G.
2004
Nonlinear stability analysis of a regular vortex pentagon outside a circle. Zbl 1252.76017
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2012
Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. Zbl 1211.76027
Kurakin, L. G.; Ostrovskaya, I. V.
2010
On the stability of discrete tripole, quadrupole, Thomson’ vortex triangle and square in a two-layer/homogeneous rotating fluid. Zbl 1346.76204
Kurakin, Leonid G.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A.
2016
On stability of a regular vortex polygon in the circular domain. Zbl 1097.76031
Kurakin, Leonid
2005
The stability of the steady rotation of a system of three equidistant vortices outside a circle. Zbl 1272.76116
Kurakin, L. G.
2011
Bifurcation of the branching of a cycle in $$n$$-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043
Kurakin, L. G.; Yudovich, V. I.
1997
On the stability of the regular $$n$$-sided polygon of vortices. Zbl 0832.76028
Kurakin, L. G.
1994
A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. Zbl 1348.76041
Kurakin, Leonid; Melekhov, Andrey; Ostrovskaya, Irina
2016
On stability of thomson’s vortex $$N$$-gon in the geostrophic model of the point Bessel vortices. Zbl 1401.76037
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2017
On the stability of Thomson’s vortex configurations inside a circular domain. Zbl 1229.37055
Kurakin, L. G.
2010
Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031
Kurakin, L. G.; Yudovich, V. I.
2000
Influence of annular boundaries on Thomson’s vortex polygon stability. Zbl 1345.70034
Kurakin, L. G.
2014
On the stability of Thomson’s vortex pentagon inside a circular domain. Zbl 1270.76018
Kurakin, Leonid G.
2012
On stability of the Thomson’s vortex $$N$$-gon in the geostrophic model of the point vortices in two-layer fluid. Zbl 1423.76076
Kurakin, Leonid G.; Lysenko, Irina A.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A.
2019
Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028
Kurakin, L. G.; Yudovich, V. I.
1986
Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry. Zbl 0953.34043
Kurakin, L. G.
1998
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 1446.76114
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2019
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040
Kurakin, L. G.; Yudovich, V. I.
2004
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 1020.37029
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025
Kurakin, L. G.; Yudovich, V. I.
2000
Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067
Kurakin, L. G.; Yudovich, V. I.
2003
Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566
Kurakin, L. G.; Yudovich, V. I.
2001
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 1324.34109
Kurakin, L. G.
2009
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521
Kurakin, L. G.; Yudovich, V. I.
2000
On the Lyapunov chain of stability criteria in the critical case of a Jordan 2-block. Zbl 0854.34052
Kurakin, L. G.
1994
On the stability of a system of two identical point vortices and a cylinder. Zbl 1459.76055
Borisov, A. V.; Kurakin, L. G.
2020
Semi-invariant form of equilibrium stability criteria for systems with one cosymmetry. Zbl 1445.34086
Kurakin, Leonid G.; Kurdoglyan, Aik V.
2019
On the stability of the orbit and the invariant set of Thomson’s vortex polygon in a two-fluid plasma. Zbl 1453.82085
Kurakin, L. G.; Lysenko, I. A.
2020
On the stability of a system of two identical point vortices and a cylinder. Zbl 1459.76055
Borisov, A. V.; Kurakin, L. G.
2020
On the stability of the orbit and the invariant set of Thomson’s vortex polygon in a two-fluid plasma. Zbl 1453.82085
Kurakin, L. G.; Lysenko, I. A.
2020
On stability of the Thomson’s vortex $$N$$-gon in the geostrophic model of the point vortices in two-layer fluid. Zbl 1423.76076
Kurakin, Leonid G.; Lysenko, Irina A.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A.
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 1446.76114
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2019
Semi-invariant form of equilibrium stability criteria for systems with one cosymmetry. Zbl 1445.34086
Kurakin, Leonid G.; Kurdoglyan, Aik V.
2019
On stability of thomson’s vortex $$N$$-gon in the geostrophic model of the point Bessel vortices. Zbl 1401.76037
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2017
On the stability of discrete tripole, quadrupole, Thomson’ vortex triangle and square in a two-layer/homogeneous rotating fluid. Zbl 1346.76204
Kurakin, Leonid G.; Ostrovskaya, Irina V.; Sokolovskiy, Mikhail A.
2016
A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. Zbl 1348.76041
Kurakin, Leonid; Melekhov, Andrey; Ostrovskaya, Irina
2016
Influence of annular boundaries on Thomson’s vortex polygon stability. Zbl 1345.70034
Kurakin, L. G.
2014
Nonlinear stability analysis of a regular vortex pentagon outside a circle. Zbl 1252.76017
Kurakin, Leonid G.; Ostrovskaya, Irina V.
2012
On the stability of Thomson’s vortex pentagon inside a circular domain. Zbl 1270.76018
Kurakin, Leonid G.
2012
The stability of the steady rotation of a system of three equidistant vortices outside a circle. Zbl 1272.76116
Kurakin, L. G.
2011
Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. Zbl 1211.76027
Kurakin, L. G.; Ostrovskaya, I. V.
2010
On the stability of Thomson’s vortex configurations inside a circular domain. Zbl 1229.37055
Kurakin, L. G.
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 1324.34109
Kurakin, L. G.
2009
On stability of a regular vortex polygon in the circular domain. Zbl 1097.76031
Kurakin, Leonid
2005
On nonlinear stability of the regular vortex systems on a sphere. Zbl 1080.76031
Kurakin, L. G.
2004
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. Zbl 1049.37040
Kurakin, L. G.; Yudovich, V. I.
2004
Codimension-1 bifurcation of the branching of two-dimensional invariant tori from a family of equilibria in systems with cosymmetry. Zbl 1067.37067
Kurakin, L. G.; Yudovich, V. I.
2003
The stability of stationary rotation of a regular vortex polygon. Zbl 1080.76520
Kurakin, L. G.; Yudovich, V. I.
2002
Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Zbl 1080.37566
Kurakin, L. G.; Yudovich, V. I.
2001
Bifurcations of a cosymmetric dynamical system with monotone loss of equilibrium stability. Zbl 1039.37031
Kurakin, L. G.; Yudovich, V. I.
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 1020.37029
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 0969.37025
Kurakin, L. G.; Yudovich, V. I.
2000
Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system. Zbl 1071.37521
Kurakin, L. G.; Yudovich, V. I.
2000
Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry. Zbl 0953.34043
Kurakin, L. G.
1998
Bifurcation of the branching of a cycle in $$n$$-parameter family of dynamic systems with cosymmetry. Zbl 0932.37043
Kurakin, L. G.; Yudovich, V. I.
1997
On the stability of the regular $$n$$-sided polygon of vortices. Zbl 0832.76028
Kurakin, L. G.
1994
On the Lyapunov chain of stability criteria in the critical case of a Jordan 2-block. Zbl 0854.34052
Kurakin, L. G.
1994
Semi-invariant form of equilibrium stability criteria in critical cases. Zbl 0632.58028
Kurakin, L. G.; Yudovich, V. I.
1986
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### Cited by 56 Authors

 22 Kurakin, Leonid Gennadievich 8 Ostrovskaya, Irina V. 6 Yudovich, Viktor Iosifovich 3 Newton, Paul K. 2 Boatto, Stefanella 2 Borisov, Alekseĭ Vladimirovich 2 Cabral, Hildeberto Eulalio 2 Carvalho, Adecarlos C. 2 Govorukhin, Vasily N. 2 Kizner, Ziv 2 Koiller, Jair 2 Kurdoglyan, Aik V. 2 Lysenko, Irina A. 2 Reinaud, Jean N. 2 Sakajo, Takashi 2 Sokolovskiy, Mikhail A. 1 Artemova, Elizaveta M. 1 Banica, Valeria 1 Bizyaev, Ivan Alekseevich 1 Cao, Daomin 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 Kim, Sun-Chul 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 Qin, Guolin 1 Ramodanov, Sergey M. 1 Ryzhov, Eugene A. 1 Shevchenko, Igor V. 1 Shnol’, Èmmanuil Èl’evich 1 Shokraneh, Houman 1 Simó, Carles 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 Zhan, Weicheng 1 Zou, Changjun
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### Cited in 22 Serials

 17 Regular and Chaotic Dynamics 6 Chaos 5 Journal of Nonlinear Science 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Nelineĭnaya Dinamika 2 Fluid Dynamics 2 Journal of Fluid Mechanics 2 Physica D 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 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
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### Cited in 12 Fields

 41 Fluid mechanics (76-XX) 17 Dynamical systems and ergodic theory (37-XX) 15 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) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)