1998

• 1.

  Borisov A. V., Lebedev V. G.

  Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering
  Regular and Chaotic Dynamics, 1998, vol. 3, no. 4, pp. 74-86
  Abstract          pdf  (657.83 Kb)

  In this article we considered the integrable problems of three vortices on a plane and sphere for noncompact case. We investigated explicitly the problems of a collapse and scattering of vortices and obtained the conditions of realization. We completed the bifurcation analysis and investigated the dependence of stability in linear approximation and frequency of rotation in relative coordinates for collinear and Thomson's configurations from value of a full moment and indicated the geometric interpretation for characteristic situations. We constructed a phase portrait and geometric projection for an integrable configuration of four vortices on a plane.

  
  

  Citation:	Borisov A. V., Lebedev V. G., Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering, Regular and Chaotic Dynamics, 1998, vol. 3, no. 4, pp. 74-86
  DOI:	10.1070/RD1998v003n04ABEH000094
  Full text:	pdf (657.83 Kb)

  Journal Info

  Impact-factor WoS (2014):	0.860
  ISSN (print):	1560-3547
  ISSN (online):	1468-4845
  Site:	http://rcd.ics.org.ru/
• 2.

  Borisov A. V., Lebedev V. G.

  Dynamics of three vortices on a plane and a sphere — II. General compact case
  Regular and Chaotic Dynamics, 1998, vol. 3, no. 2, pp. 99-114
  Abstract          pdf  (493.96 Kb)

  Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using the variables introduced in previous part of the work.

  
  

  Citation:	Borisov A. V., Lebedev V. G., Dynamics of three vortices on a plane and a sphere — II. General compact case, Regular and Chaotic Dynamics, 1998, vol. 3, no. 2, pp. 99-114
  DOI:	10.1070/RD1998v003n02ABEH000075
  Full text:	pdf (493.96 Kb)

  Journal Info

  Impact-factor WoS (2014):	0.860
  ISSN (print):	1560-3547
  ISSN (online):	1468-4845
  Site:	http://rcd.ics.org.ru/