a discussio n o f the ring s of Saturn. I n Chap . 4, the issu e involves collisions.
The concludin g Chap . 5 discusses the likelihoo d o f "ba d thing s happening. "
Everyone, fro m novice s to experts , wil l find something new .
Some result s ar e new , whil e other s hav e bee n presente d earlie r (e.g. , a t
colloquia, Oberwolfac h meetings--particularl y severa l durin g th e 1970s—
Midwest Dynamica l System s meetings, a 1983 month long mini-course given
in Receife , Brazi l whil e visitin g Hildebert o Cabral , i n a serie s o f lecture s
in Pari s ove r 1985-87 hoste d b y Michae l Herman , severa l informa l lecture s
during 1989 in Barcelona hosted b y Jaume Llibre, etc.,) an d even advertise d
as "wil l appear " i n full y intende d bu t neve r complete d papers . I n othe r
words, man y o f thes e result s hav e no t bee n previousl y published . A s mos t
authors o f a boo k quickl y discover , th e har d par t i s no t t o decid e wha t
to include , bu t wha t t o exclude—particularl y i f a boo k i s to b e eventuall y
completed. (Som e of the exclude d materia l probabl y wil l appear i n [90]. )
Other result s describe d i n thi s boo k com e fro m m y earlie r papers . Th e
particular journal s tha t publishe d thes e papers ar e implicitl y acknowledge d
and thanke d vi a th e references . Bu t m y expositor y pape r [88 ] "A visit to
the Newtonian n-body via elementary complex variables" i s extensively use d
to provid e structur e an d motivatio n fo r a coupl e o f th e chapters , particu -
larly th e introductor y one , so I want t o explicitl y than k th e MA A fo r thei r
permission t o us e i t i n this manner .
My dee p thank s an d appreciatio n g o t o Patric k Coulton , th e chai r fo r
this particula r CBM S conference, an d m y long-time frien d Gregor y Galpri n
for invitin g m e t o b e th e CBM S lecture r an d fo r thei r effort s t o assembl e
a successfu l CBM S application . I als o than k the m fo r thei r ful l an d activ e
participation i n all lectures an d extr a session s that the y helpe d t o organize ,
and for everything they did to make the stay so enjoyable fo r all of us. I want
to than k al l o f the participant s fo r keepin g th e worksho p session s s o lively!
My thank s t o th e Mathematic s Departmen t a t Easter n Illinoi s Universit y
for thei r graciou s hospitality . M y thank s t o Ro n Rosie r an d th e CBM S
for thei r progra m tha t make s thes e kind s o f lecture s possible . Thank s t o
Neal Hulkower : twic e a t Northwester n h e too k m y yea r lon g cours e o n th e
Newtonian iV-bod y problem (th e first in 1969-70), and he still had both set s
of lectur e notes ! Hi s note s prove d t o b e usefu l i n recoverin g som e o f m y
earlier result s an d arguments . Als o thanks t o anothe r studen t (bu t I do no t
recall wh o i t was ) wh o gav e m e a cop y o f his notes man y year s ago .
Irvine, Californi a
January, 200 5
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