THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY

1987 ◽  
Vol 29 (3) ◽  
pp. 629-658 ◽  
Author(s):  
A T Fomenko
Keyword(s):  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Constant Energy

STOCHASTIC VERSIONS OF ANOSOV'S AND NEISTADT'S THEOREMS ON AVERAGING

2001 ◽  
Vol 01 (01) ◽  
pp. 1-21 ◽  
Author(s):  
YURI KIFER
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hamiltonian Systems ◽  
Initial Conditions ◽  
Slow Motion ◽  
Averaging Principle ◽  
Integrable Hamiltonian Systems ◽  
Constant Energy ◽  
Slow Motions ◽  
Fast And Slow Motions

In systems which combine slow and fast motions the averaging principle says that a good approximation of the slow motion can be obtained by averaging its parameters in fast variables. This setup arises, for instance, in perturbations of Hamiltonian systems where motions on constant energy manifolds are fast and across them are slow. When these perturbations are deterministic Anosov's theorem says that the averaging principle works except for a small in measure set of initial conditions while Neistadt's theorem gives error estimates in the case of perturbations of integrable Hamiltonian systems. These results are extended here to the case of fast and slow motions given by stochastic differential equations.

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
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