PAPERS FOR THE N BODY SEMINAR. STANFORD. 2003. 

<br>
<br>            

<b> Quick and  telegraphic as opposed to
encylopaedic tomes. </b>
<br> 
Introduction to the N-body problem.  Chenciner. 1997 `Ravello' notes.
<br>
A l'infini en temps fini. Chenciner.  Bourbaki seminar.
<br>
Rick Moeckel, {\sl Some qualitative features of the three-body
problem, Contemporary Mathematics}, vol. 81, 1-21, (1988) 
<br> 
Pollard. Celestial mechanics.  
<br>
Goroff's introduction to the English Translation of Poincare's
Les methodes nouvelles de la mecanique celeste.

<br>
<br>            


{\bf General texts   on the classical N-body problem.}
<br>

Pollard: short, telegraphic, good overview of foundational material.
<br>
Birkhoff. Last ch. of his `Dynamical Systems'.
<br>
 Siegel-Moser: Lectures on Celestial Mechanics. an analytic standard. 
<br>
Marchall: The three-body problem.  encyclopaedic.
<br>
Poincare.  Les Methodes Nouvelles de la mecanique celeste. 

<br>

<b> Open Problem Lists </b>

<br>

<A> 
http://www.aimath.org/WWN/varcelest/ 
AIM </A>

being one result of the June AIM conference on
variational methods in celestial mechanics. 
<br>

the end of M. Herman's 1998 ICM paper. 

\vskip .3cm 

<br>
<br>            


<b>MORE SPECIALIZED towards variational methods. </b>
 
{\bf Papers on the classical N-body problem focussing on variational methods.}

Ferrario and Terracini:
math-ph/0302022 On the Existence of Collisionless Equivariant Minimizers for the Classical n-body
Problem. Davide L.     Ferrario, Susanna Terracini. 58 pages. MP (DS). 
<b> THE PAPER WE WILL GO THROUGH </b>
Perhaps the best work in the field over  last year .  
We will try to go through this by lecture 4 or 5. 

<br>
Supporting material:    Chenciner's 2002 ICM paper(s) where he proves
via Marchall's method, that action minimizers for the fixed ends problem
admit  no internal collisions.  See further below

<br>
<br>





<b> Montgomery: </b>

2000 
A remarkable periodic solution of the three-body problem
 in the case of equal masses Annals of Mathematics, v. 152, 881-901, Nov. 2000. 
Montgomery and Chenciner
 
<br>

1998 
The N-body problem, the braid group, and action-minimizing periodic orbits, 
Nonlinearity, vol. 11, no. 2, 363-376, 1998. 


 <br>

<br>
<br>

<b>Chenciner: </b> 
Most available at:
<br>
http://www.imcce.fr/Equipes/ASD/person/chenciner/chen_preprint.html

 2003
              SYMMETRIES AND ``SIMPLE" SOLUTIONS OF THE CLASSICAL N-BODY PROBLEM
              Alain Chenciner
              ICMP, Lisbonne juillet 2003, Proceedings a para”tre chez World Scientific
   
<br>           

       2002
               Action minimizing solutions of the Newtonian n-body problem
              Alain Chenciner
              Abstract ICM, Pˇkin aout 2002
              
<br>
              Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry
              Alain Chenciner
              ICM, Pˇkin aout 2002

<br>
               
              
              Some facts and more questions about the ``Eight" (version 26-09-02)
              Alain Chenciner
              Proceedings of the confˇrence ``Nonlinear functional analysis",
              Taiyuan 14-18 aout 2002 (World Scientific, in press)
               
<br>

              Minima de l'intˇgrale d'action du Probl¸me newtonien de 4
             corps de masses ˇgales dans R^3 : orbites "hip-hop",
              with Andrea Venturelli, 
              Celestial Mechanics, vol. 77, pp.139-152 (2000)
              (preprint : pdf, 304 ko)
               

<br>
       1998 
              Collisions totales, mouvements compl¸tement paraboliques et rˇduction des
               homothˇties dans le probl¸me des n corps.
              Alain Chenciner
              paru dans Regular and chaotic dynamics, V.3, 3, pp.93-106 (1998)

<br>
             
       1997 
              Le probl¸me des n corps et les distances mutuelles,
              with Alain Albouy ,
              Inventiones mathematicae 131 pp. 151-184 (1998)

<br>
              

              Introduction to the N-body problem.(ˇcole d'ˇtˇ de Ravello)