Preface
Mathematical billiards describe the motion of a mass
main with elastic reflections from the boundary. Bil
single mathematical theory; to quote from [57], it is
ematician's playground where various methods and a
tested and honed. Billiards is indeed a very popular s
uary of 2005, MathSciNet gave more than 1,400 entries
anywhere in the database. The number of physical pap
billiards could easily be equally substantial.
Usually billiards are studied in the framework of
dynamical systems. This book emphasizes connection
and to physics, and billiards are treated here in their
geometrical optics. In particular, the book contains abo
There are a number of surveys devoted to mathema
from popular to technically involved: [41, 43, 46, 57,
My interest in mathematical billiards started wh
man, I was reading [102], whose first Russian edition (1
eight pages devoted to billiards. I hope the present bo
undergraduate and graduate students to this beautiful
ject; at least, I tried to write a book that I would enjoy
undergraduate.
This book can serve as a basis for an advanced un
a graduate topics course. There is more material her
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