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The Existence of Transverse Homoclinic Points in the Sitnikov Problem

โœ Scribed by H. Dankowicz; P. Holmes

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
511 KB
Volume
116
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

Using Melnikov's method we are able to prove the existence of transverse homoclinic orbits and therefore the existence of a horseshoe in a special restricted three-body problem. This analysis is an alternative to the one described by Moser " "Stable and Random Motions in Dynamical Systems," Princeton Univ. Press. Princeton. NJ, 1973), based on Sitnikov's original work (Dokl. Akad. Nauk. USSR 133. No. 2 (1960), 303 306). where the task is accomplished using a more direct construction of the horseshoe. I 1495 Acadenic Press. Inc.

๐Ÿ“œ SIMILAR VOLUMES

The Existence of Transverse Homoclinic S
The Existence of Transverse Homoclinic Solutions for Higher Order Equations
โœ Joseph Gruendler ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 606 KB

Differential equations are considered which contain a small parameter. When the parameter is zero the equation is autonomous with a hyperbolic equilibrium and a homoclinic solution. No restriction is placed on the dimension of the phase space or the dimension of intersection of the stable and unstab