Info on Dynamical Systems and Sitnikov Problem

[l'Hôpital]

Hey guys.

I'll be doing my first research project with a professor and although the details are a bit unclear, he gave me the topic at hand and the problem we'll be tackling: the Sitnikov problem.

To quote him,

I don't have a detailed project in mind yet although something about the "last invariant curve" and the relation to the "homoclinic chaos at infinity" might be fun.

He also suggested that I should learn about the following topics:

Poincare maps for time-periodic ODEs, area preserving maps, fixed and periodic points and their stability analysis and continuation theory, invariant curves, homoclinic chaos.

I'm currently working from Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Hall and Meyer. I read like the first 50 pages, then I just started picking the book apart for the stuff in the latter quotes. However, some of it is a bit unclear and some of the topics are not in the book (these are boldened), thus leaving me searching for more sources.

I was wondering if anyone knew of any good books/pdf/article/etc. on these topics, or perhaps on the Sitnikov problem. I could use the help.

 

[Pinu7]

Vladamir Arnold's Mathematical Aspects of Classical and Celestial Mechanics (NOT to be confused with Mathematical Methods of Classical Mechanics) is, by far, the most authoritative text on mechanical systems. I think he covers all of the stuff you bolded.

In addition, Giovanni Gallavotti's Elements of Mechanics may be helpful. (Found Here: http://ipparco.roma1.infn.it/pagine/2008.html)


A couple related articles by J. Moser comes in mind:

J. Moser- On invariant curves of area-preserving mappings of an annulus. (1962)
As well has his responce

J. Moser- Remark on the paper “On invariant curves of area-preserving mappings
of an annulus”. (2001)