Stability and KAM Theory

2009 ◽  
pp. 329-354
Author(s):  
Kenneth Meyer ◽  
Glen Hall ◽  
Dan Offin
Keyword(s):  
Kam Theory

scholarly journals Converse KAM: Theory and practice

1985 ◽  
Vol 98 (4) ◽  
pp. 469-512 ◽  
Author(s):  
R. S. MacKay ◽  
I. C. Percival
Keyword(s):  
Kam Theory ◽  
Theory And Practice

Survey on dissipative KAM theory including quasi-periodic bifurcation theory (H. Broer)

2005 ◽  
pp. 303-356 ◽  
Author(s):  
Maria-Cristina Ciocci ◽  
Anna Litvak-Hinenzon ◽  
Henk Broer
Keyword(s):  
Bifurcation Theory ◽  
Kam Theory ◽  
Periodic Bifurcation

scholarly journals A note on KAM theory for quasi-linear and fully nonlinear forced KdV

2013 ◽  
Vol 24 (3) ◽  
pp. 437-450 ◽  
Author(s):  
Pietro Baldi ◽  
Massimiliano Berti ◽  
Riccardo Montalto
Keyword(s):  
Kam Theory ◽  
Fully Nonlinear

The finite-dimensional reversible KAM theory

1998 ◽  
Vol 112 (1-2) ◽  
pp. 132-147 ◽  
Author(s):  
M.B. Sevryuk
Keyword(s):  
Kam Theory ◽  
Finite Dimensional

Anderson Localization and KAM-Theory

1990 ◽  
pp. 237-249 ◽  
Author(s):  
V.A. Chulaevsky ◽  
Ya.G. Sinai
Keyword(s):  
Anderson Localization ◽  
Kam Theory

scholarly journals Nekhoroshev-Stability ofL4andL5in the Spatial Restricted Problem

1999 ◽  
Vol 172 ◽  
pp. 445-446 ◽  
Author(s):  
Giancarlo Benettin ◽  
Francesco Fassò ◽  
Massimiliano Guzzo
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Critical Mass ◽  
Kam Theory ◽  
Birkhoff Normal Form ◽  
Three Body Problem ◽  
Arnold Diffusion ◽  
Convexity Assumption ◽  
Three Body ◽  
Nekhoroshev Stability

The Lagrangian equilateral pointsL4andL5of the restricted circular three-body problem are elliptic for all values of the reduced massμbelow Routh’s critical massμR≈ .0385. In the spatial case, because of the possibility of Arnold diffusion, KAM theory does not provide Lyapunov-stability. Nevertheless, one can consider the so-called ‘Nekhoroshev-stability’: denoting byda convenient distance from the equilibrium point, one asks whetherfor any small єe > 0, with positiveaandb. Until recently this problem, as more generally the problem of Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems, was studied only under some arithmetic conditions on the frequencies, and thus onμ(see e.g .Giorgilli, 1989). Our aim was instead considering all values ofμup toμR. As a matter of fact, Nekhoroshev-stability of elliptic equilibria, without any arithmetic assumption on the frequencies, was proved recently under the hypothesis that the fourth order Birkhoff normal form of the Hamiltonian exists and satisfies a ‘quasi-convexity’ assumption (Fassòet al, 1998; Guzzoet al, 1998; Niedermann, 1998).

KAM theory

2013 ◽  
pp. 149-158
Author(s):  
S. G. Rajeev
Keyword(s):  
Kam Theory
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