A new method to construct integrable approximations to nearly integrable systems in Celestial Mechanics: application to the Sitnikov problem

2015 ◽  
Vol 122 (2) ◽  
pp. 101-116 ◽  
Author(s):  
Johannes Hagel
Keyword(s):  
Celestial Mechanics ◽  
Integrable Systems ◽  
New Method ◽  
Sitnikov Problem ◽  
Nearly Integrable Systems

Normal form construction for nearly-integrable systems with dissipation

2012 ◽  
Vol 17 (3-4) ◽  
pp. 273-292 ◽  
Author(s):  
Aessandra Celletti ◽  
Christoph Lhotka
Keyword(s):  
Normal Form ◽  
Integrable Systems ◽  
Nearly Integrable Systems

scholarly journals Asymptotic velocity for four celestial bodies

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170426
Author(s):  
Andreas Knauf
Keyword(s):  
Celestial Mechanics ◽  
Integrable Systems ◽  
Energy Surface ◽  
Initial Conditions ◽  
Theme Issue ◽  
Asymptotic Velocity ◽  
Pair Potentials ◽  
Finite Dimensional ◽  
Celestial Bodies ◽  
Almost All

Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree − α for α ∈(0, 2), that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and almost all initial conditions on the energy surface. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

Dynamics of solitons in nearly integrable systems

1989 ◽  
Vol 61 (4) ◽  
pp. 763-915 ◽  
Author(s):  
Yuri S. Kivshar ◽  
Boris A. Malomed
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems

scholarly journals Recurrence of fidelity in nearly integrable systems

2003 ◽  
Vol 68 (3) ◽  
Author(s):  
R. Sankaranarayanan ◽  
Arul Lakshminarayan
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems

Addendum: Dynamics of solitons in nearly integrable systems

1991 ◽  
Vol 63 (1) ◽  
pp. 211-211 ◽  
Author(s):  
Yuri S. Kivshar ◽  
Boris A. Malomed
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems
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