scholarly journals Bifurcations of Liouville tori in elliptical billiards

2009 ◽  
Vol 14 (4-5) ◽  
pp. 479-494 ◽  
Author(s):  
V. Dragović ◽  
M. Radnović
Keyword(s):  
Liouville Tori

BIFURCATIONS OF THE COMMON LEVEL SETS OF ATOMIC HYDROGEN IN VAN DER WAALS POTENTIAL

2003 ◽  
Vol 13 (01) ◽  
pp. 107-114 ◽  
Author(s):  
J. KHARBACH ◽  
S. DEKKAKI ◽  
A. T.-H. OUAZZANI ◽  
M. OUAZZANI-JAMIL
Keyword(s):  
Level Sets ◽  
Van Der Waals ◽  
Space Structure ◽  
Classical Dynamics ◽  
Anharmonic Oscillators ◽  
Numerical Investigations ◽  
System Parameters ◽  
Phase Space Structure ◽  
Liouville Tori ◽  
The Common

The classical dynamics of a hydrogen atom in a generalized van der Waals potential is investigated. In order to carry out the analytical and numerical investigations for a range of parametric values, we removed the singularity of the problem using Levi–Civita regularization and converted the problem into that of two coupled sextic anharmonic oscillators. We give a complete description of the real phase space structure of the converted system and give also an explicit periodic solution for singular common-level sets of the first integrals. All generic bifurcations of Liouville tori were determined theoretically. Numerical investigations are carried out for all generic bifurcations and we observe chaos-order-chaos transition when one of the system parameters is varied.

scholarly journals Non-degenerate Liouville tori are KAM stable

2016 ◽  
Vol 292 ◽  
pp. 42-51 ◽  
Author(s):  
Abed Bounemoura
Keyword(s):  
Liouville Tori

Bifurcation diagrams and Fomenko's Surgery on Liouville tori of a rigid body in the Goryachev-Chaplygin case on sokolov terms

2018 ◽  
Vol 7 (4) ◽  
pp. 437-449
Author(s):  
Jaouad Kharbach ◽  
Mohammed Benkhali ◽  
Walid Chatar ◽  
Ahmed Sali ◽  
Abdellah Rezzouk ◽  
...  
Keyword(s):  
Rigid Body ◽  
Bifurcation Diagrams ◽  
Liouville Tori

scholarly journals On bifurcation of the four Liouville tori in one generalized integrable model of the vortex dynamics

2019 ◽  
Vol 487 (4) ◽  
pp. 376-380
Author(s):  
P. E. Ryabov
Keyword(s):  
Bifurcation Diagram ◽  
Vortex Dynamics ◽  
Integrable Model ◽  
Vortex Pair ◽  
Einstein Condensate ◽  
Point Vortices ◽  
Physical Parameters ◽  
Bose Einstein Condensate ◽  
Liouville Tori ◽  
The Stability

The article deals with a generalized mathematical model of the dynamics of two point vortices in the Bose-Einstein condensate enclosed in a harmonic trap, and of the dynamics of two point vortices in an ideal fluid bounded by a circular region. In the case of a positive vortex pair, which is of interest for physical experimental applications, a new bifurcation diagram is obtained, for which the bifurcation of four tori into one is indicated. The presence of bifurcations of three and four tori in the integrable model of vortex dynamics with positive intensities indicates a complex transition and the connection of bifurcation diagrams of both limit cases. Analytical results of this publication (the bifurcation diagram, the reduction to a system with one degree of freedom, the stability analysis) form the basis of computer simulation of absolute dynamics of vortices in a fixed coordinate system in the case of arbitrary values of the physical parameters of the model (the intensities, the vortex interaction and etc.).

Sign in / Sign up

Export Citation Format

Share Document