Translator Disclaimer
15 August 2011 Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
Joseph Galante, Vadim Kaloshin
Author Affiliations +
Duke Math. J. 159(2): 275-327 (15 August 2011). DOI: 10.1215/00127094-1415878


The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle along with Aubry-Mather theory to construct (Birkhoff) regions of instability for a certain three-body problem, given by a Hamiltonian system of 2 degrees of freedom. We believe that these methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show the existence of instabilities for the orbit of the comet. In particular, we show that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper, we extend the result to beyond e=1 and show the existence of ejection orbits. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity.


Download Citation

Joseph Galante. Vadim Kaloshin. "Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action." Duke Math. J. 159 (2) 275 - 327, 15 August 2011.


Published: 15 August 2011
First available in Project Euclid: 4 August 2011

zbMATH: 1269.70016
MathSciNet: MR2824484
Digital Object Identifier: 10.1215/00127094-1415878

Primary: 37J50 , 70F07 , 70F15
Secondary: 37E40 , 37J25 , 37J45 , 37M99

Rights: Copyright © 2011 Duke University Press


This article is only available to subscribers.
It is not available for individual sale.

Vol.159 • No. 2 • 15 August 2011
Back to Top