scholarly journals The speed of Arnold diffusion

2013 ◽  
Vol 251 ◽  
pp. 19-38 ◽  
Author(s):  
C. Efthymiopoulos ◽  
M. Harsoula
Keyword(s):  
Arnold Diffusion

scholarly journals Arnold diffusion in the swing equations of a power system

1984 ◽  
Vol 31 (8) ◽  
pp. 673-688 ◽  
Author(s):  
F. Salam ◽  
J. Marsden ◽  
P. Varaiya
Keyword(s):  
Power System ◽  
Arnold Diffusion

scholarly journals Semi-analytic Computations of the Speed of Arnold Diffusion Along Single Resonances in A Priori Stable Hamiltonian Systems

2019 ◽  
Vol 30 (3) ◽  
pp. 851-901
Author(s):  
Massimiliano Guzzo ◽  
Christos Efthymiopoulos ◽  
Rocío I. Paez
Keyword(s):  
Hamiltonian Systems ◽  
A Priori ◽  
Arnold Diffusion

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).

Searches for "Arnold Diffusion" and "Chaotic" Motion in the Beam-Bean Interaction

1983 ◽  
Vol 30 (4) ◽  
pp. 2427-2429 ◽  
Author(s):  
D. Neuffer ◽  
A. Riddiford ◽  
A. G. Ruggiero
Keyword(s):  
Chaotic Motion ◽  
Arnold Diffusion

Detection of Arnold diffusion in Hamiltonian systems

2003 ◽  
Vol 182 (3-4) ◽  
pp. 179-187 ◽  
Author(s):  
Elena Lega ◽  
Massimiliano Guzzo ◽  
Claude Froeschlé
Keyword(s):  
Hamiltonian Systems ◽  
Arnold Diffusion

scholarly journals Theory of fast arnold diffusion in many-frequency systems

1993 ◽  
Vol 71 (1-2) ◽  
pp. 243-258 ◽  
Author(s):  
B. V. Chirikov ◽  
V. V. Vecheslavov
Keyword(s):  
Arnold Diffusion
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