scholarly journals Existence of KAM Tori in Degenerate Hamiltonian Systems

1994 ◽  
Vol 114 (1) ◽  
pp. 288-335 ◽  
Author(s):  
C.Q. Cheng ◽  
Y.S. Sun
Keyword(s):  
Hamiltonian Systems ◽  
Kam Tori ◽  
Degenerate Hamiltonian Systems

Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori

2011 ◽  
Vol 10 (3) ◽  
pp. 817-856 ◽  
Author(s):  
Kenneth R. Meyer ◽  
Jesús F. Palacián ◽  
Patricia Yanguas
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Kam Tori

Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems

Nonlinearity ◽  
2017 ◽  
Vol 30 (8) ◽  
pp. 3151-3202 ◽  
Author(s):  
Renato C Calleja ◽  
Alessandra Celletti ◽  
Rafael de la Llave
Keyword(s):  
Hamiltonian Systems ◽  
Kam Tori

scholarly journals Topological obstacles to the realizability of integrable Hamiltonian systems by billiards

2019 ◽  
Vol 488 (5) ◽  
pp. 471-475
Author(s):  
V. V. Vedyushkina ◽  
A. T. Fomenko
Keyword(s):  
Magnetic Field ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Degenerate Hamiltonian Systems ◽  
Liouville Equivalence

We introduce the following classes of integrable billiards: elementary billiards, topological, books, with potential, magnetic field, geodesic billiards. These classes are used to test the A.T. Fomenko conjecture about the realizability up to Liouville equivalence by billiards of integrable non-degenerate Hamiltonian systems with two degrees of freedom. In the class of book billiards found topological obstacles to realizability.

LOCALIZING TRANSPORT BARRIERS IN DEGENERATE 3/2 D.O.F. HAMILTONIAN SYSTEMS WITH APPLICATIONS TO MAGNETIC CONFINEMENT FUSION

2013 ◽  
Vol 23 (02) ◽  
pp. 1350034 ◽  
Author(s):  
DANA CONSTANTINESCU ◽  
MARIE-CHRISTINE FIRPO
Keyword(s):  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Magnetic Confinement ◽  
Tokamak Plasmas ◽  
Transport Barrier ◽  
Magnetic Confinement Fusion ◽  
Hamiltonian Models ◽  
Transport Barriers ◽  
Confinement Fusion ◽  
Degenerate Hamiltonian Systems

The existence of transport barriers in 3/2 degrees of freedom degenerate Hamiltonian systems is studied using the associated stroboscopic maps. For small enough amplitudes of the perturbations, a transport barrier (formed by infinitely many invariant rotational circles) is proven to exist and to form in the degenerate annulus. These results are applied to Hamiltonian models which describe some magnetic configurations in tokamak plasmas.

scholarly journals Geometry of KAM tori for nearly integrable Hamiltonian systems

2007 ◽  
Vol 27 (03) ◽  
pp. 725 ◽  
Author(s):  
HENK BROER ◽  
RICHARD CUSHMAN ◽  
FRANCESCO FASSÒ ◽  
FLORIS TAKENS
Keyword(s):  
Hamiltonian Systems ◽  
Kam Tori ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems

scholarly journals Brouwer’s satellite solution redux

2021 ◽  
Vol 133 (10) ◽  
Author(s):  
Martin Lara
Keyword(s):  
Hamiltonian Systems ◽  
Artificial Satellite ◽  
Hamiltonian Reduction ◽  
Theoretical Interest ◽  
Keplerian Motion ◽  
New Approach ◽  
Satellite Problem ◽  
Satellite Solution ◽  
Degenerate Hamiltonian Systems ◽  
Single Set

AbstractBrouwer’s solution to the artificial satellite problem is revisited. We show that the complete Hamiltonian reduction is rather achieved in the plain Poincaré’s style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel’s alternative for dealing with perturbed degenerate Hamiltonian systems. Beyond the theoretical interest of the new approach as regards the complete reduction of perturbed Keplerian motion, we also show that a solution based on a single set of corrections may yield computational benefits in the implementation of an analytic orbit propagator.

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