Transverse Foliations to Nonsingular Morse–Smale Flows on the 3-Sphere and Bott-Integrable Hamiltonian Systems

2008 ◽  
Vol 7 (2) ◽  
pp. 411-415
Author(s):  
Michael C. Sullivan
Keyword(s):  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Smale Flows

KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN SYSTEMS

1998 ◽  
Vol 07 (02) ◽  
pp. 123-153 ◽  
Author(s):  
J. CASASAYAS ◽  
J. MARTINEZ ALFARO ◽  
A. NUNES
Keyword(s):  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Energy Levels ◽  
Solid Torus ◽  
Integrable Hamiltonian Systems ◽  
Hamiltonian Flows ◽  
Smale Flows ◽  
Knots And Links

The main purpose of this paper is to prove that Bott integrable Hamiltonian flows and non-singular Morse-Smale flows are closely related. As a consequence, we obtain a classification of the knots and links formed by periodic orbits of Bott integrable Hamiltonians on the 3-sphere and on the solid torus. We also show that most of Fomenko's theory on the topology of the energy levels of Bott integrable Hamiltonians can be derived from Morgan's results on 3-manifolds that admit non-singular Morse-Smale flows.

Effects of symmetry on instability-driven chaotic energy transport in near-integrable, Hamiltonian systems

1994 ◽  
Vol 37 (4-5) ◽  
pp. 323-339 ◽  
Author(s):  
M.Gregory Forest ◽  
Christopher G. Goedde ◽  
Amarendra Sinha
Keyword(s):  
Hamiltonian Systems ◽  
Energy Transport ◽  
Integrable Hamiltonian Systems

scholarly journals Two-Photon Algebra and Integrable Hamiltonian Systems

2001 ◽  
Vol 8 (sup1) ◽  
pp. 18-22 ◽  
Author(s):  
Angel Ballesteros ◽  
Francisco J Herranz
Keyword(s):  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Two Photon

Geometric quantization of Neumann‐type completely integrable Hamiltonian systems

1994 ◽  
Vol 35 (4) ◽  
pp. 1532-1548 ◽  
Author(s):  
I. V. Mykytiuk ◽  
A. K. Prykarpatsky ◽  
R. I. Andrushkiw ◽  
V. Hr. Samoilenko
Keyword(s):  
Hamiltonian Systems ◽  
Geometric Quantization ◽  
Integrable Hamiltonian Systems ◽  
Completely Integrable ◽  
Neumann Type ◽  
Completely Integrable Hamiltonian Systems
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