Sergei Tabachnikov, Committee Chair/Co-Chair Mark Levi, Committee Member Yakov B Pesin, Committee Member Howard Weiss, Committee Member Elena Katok, Committee Member Nigel David Higson, Committee Member
Keywords:
dynamical systems outer billiards hyperbolicity chaos piecewise-isometry complexity
Abstract:
This thesis explores two quite different types of dynamics occurring in outer
billiards. First, we construct the first example of a hyperbolic outer
billiard. Thus settling the question of whether chaotic outer billiards
exist. The much more regular (quasi-periodic) dynamics for a certain class
of quadrilaterals is considered next. Some results on complexity growth and
boundedness of orbits are obtained from symbolic dynamical description of
the mapping. In conclusion, we present numerical studies of outer billiard
systems extending the the above examples.
