Billiards - Geometry and dynamics, first steps (1-2 credits)
12.2. - 26.2.2016 (updated 24.2.2016)
Erasmus exchange teacher, professor Eric Lehman, gives a course on "Billiards
- Geometry and dynamics, first steps" in February.
Mathematical billiards describe the motion of a mass point in a domain
with elastic reflections from the boundary.
Billiards is not a single mathematical theory, it is rather a mathematician’s
playground
where various methods and approaches are tested and honed.
Usually billiards are studied in the framework of the theory of dynamical
systems.
Here we emphasize connections to geometry and to physics,
and billiards are treated here in their relation with geometrical optics.
We hope the course will attract undergraduate and graduate students
to
this beautiful and rich subject!
The chapters will be mostly independent of each other in such a way
that if one has missed some lectures, it will always be possible to understand
the following lectures anyway.
Teacher: Professors Eric Lehman (emeritus, Université de Caen,
France)
Local coordinator: Martti Pesonen (Educa E219)
Course main www-page (this page):
http://wanda.uef.fi/matematiikka/kurssit/Billiards-geometry/
Course material: Eric follows loosely the book
https://www.math.psu.edu/tabachni/Books/billiardsgeometry.pdf
Lecture notes
Chapter 1, Chapter
2, Chapter 3
Exercise sheet 1, Exercise
sheet 2, Exercise sheet 3
See the revised schedule:
All class reservations are to classroom E202.
Time-table (version 24.2.1016)
| Time |
Mondays |
Tuesday 16. (and 23.2.?) |
Wednesday 24.2.) |
Thursdays 18. and 25.2. |
Friday 12.2. |
| 12-13 |
|
|
|
|
|
| 13-14 |
|
|
|
|
Billiards geometry (ei 19.2.) |
| 14-15 |
|
|
|
|
Billiards geometry (ei 19.2.) |
| 15-16 |
|
|
|
|
|
| 16.00-17 |
|
Billiards geometry |
Billiards geometry |
Billiards geometry |
|
| 17-18 |
|
Billiards geometry |
Billiards geometry |
Billiards geometry |
|
| 18-19 |
|
Billiards geometry |
|
Billiards geometry |
|
Latest courses:
Differential
Projective Geometry and Schwarzian Derivative 2015
Hyperbolic Geometry 2014
Spherical Geometry 2012
Information: Lehman or Pesonen
eric.lehman {cat tail} unicaen.fr
martti.pesonen {cat tail} uef.fi