Preface
This boo k i s the writte n versio n o f m y Conferenc e Boar d o f Mathematica l
Sciences (CBMS ) lecture s presente d durin g th e wee k o f Jun e 10, 2002 , a t
Eastern Illinoi s University i n Charleston , Illinois . Th e te n lecture s centere d
on my first an d persisten t academi c love—th e Newtonia n iV-bod y problem .
While some experts activel y participate d i n the sessions, this conferenc e
fully live d up to the intent o f the CBM S series in that mos t o f the attendee s
were graduate students , new-comer s to the field, or curious mathematician s
wishing t o lear n somethin g abou t thi s fascinatin g topic . Accordingly , th e
goals o f th e lecture s quickl y change d fro m a technica l presentatio n appro -
priate primaril y fo r "experts, " t o presentation s no w intende d t o introduc e
everyone t o th e basi c structur e o f AT-bod y systems, t o identif y certai n per -
sistent researc h themes, and , hopefully , t o recruit activ e participants t o thi s
fascinating researc h area . A s such , durin g eac h lectur e severa l unsolve d
research problem s wer e described: som e o f them ar e include d here .
The ne w goal s fo r th e lecture s change d th e nature , content , expositor y
tone, an d eve n th e subjec t matte r t o mak e th e presentation s mor e respon -
sive to the specifi c interest s o f the participant s whil e addressin g their man y
questions, Fo r instance , I include d mor e introductor y materia l tha n origi -
nally planned : i n retrospect, thi s wa s a n excellen t addition .
The conten t an d approac h o f this boo k mimi c th e change d goal s o f th e
lectures; e.g., i n addition t o new material, yo u will find discussions intende d
to develo p intuition , introductor y material , occasiona l anecdotes , an d de -
scriptions o f open problems . T o provide cohesio n fo r eac h chapter , som e of
the materia l revolve s abou t unsolve d researc h problems—wher e th e moti -
vating rol e o f th e proble m ma y b e o f mor e valu e tha n th e actua l problem .
In Chap. 1, for instance, much of the discussion is intended to lead to an un-
resolved issu e abou t th e weir d dynamic s exhibite d i n th e F-rin g o f Saturn .
In Chap . 2 , th e discussio n i s tie d togethe r vi a a conjectur e involvin g th e
diameter o f the AT-bod y system. I n Chap . 3 , the unifyin g problem s involv e
the important issu e of finding certain AT-bod y configurations, whic h leads t o
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