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Symbolic dynamics of almost collision orbits and skew products of symplectic maps

Sergey Bolotin

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Recommended by A Chenciner

We prove the existence of chaotic almost collision orbits of the plane restricted elliptic 3-body problem with small mass ratio and eccentricity shadowing chains of collision orbits of Kepler's problem. The proof is based on the dynamics of random compositions of nearly integrable symplectic maps.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

95.10.Ce Celestial mechanics (including n-body problems) (see also 45.50.Pk in classical mechanics of discrete systems)

45.50.Tn Collisions

45.50.Pk Celestial mechanics

45.50.Jf Few- and many-body systems

MSC

70K55 Transition to stochasticity (chaotic behavior) (See also 37D45)

70F16 Collisions in celestial mechanics, regularization

37D45 Strange attractors, chaotic dynamics

70F07 Three-body problems

70F15 Celestial mechanics

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Astrophysics and astroparticles

Dates

Issue 9 (September 2006)

Received 27 March 2006, in final form 5 July 2006

Published 27 July 2006



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