Mathematical billiards describe the motion of a mass point in a domain with elastic
reflections off the boundary or, equivalently, the behavior of rays of light in a domain with …

Purpose: To describe tear function, mucin alterations, and ocular surface disorder in patients
with atopic diseases. Methods: Subjects underwent corneal sensitivity measurements …

Abstract CONTENTS Introduction § 1. Bisecting property § 2. Generating function and
periodic points § 3. Several modifications of the dual billiard map § 4. Duality between …

We discuss the dynamics of a class of non-ergodic piecewise affine maps of the torus. These
maps exhibit highly complex and little understood behavior. We present computer graphics …

Let X be a region of ${\rm\bf R}\sp {N} $ and ${\cal P}=\{P\sb0,\..., P\sb {r-1}\} $ a finite $(r> 1)
$ partition of X such that each $ P\sb {i} $ has positive Lebesgue measure. A map $ T:\X\to X …

Let y be a smooth closed convex curve in the plane with positive curvature and. v be a point
outside of it. There are two tangent lines to y through л; choose one of them and reflect. v in …

With a plane closed convex curve, T, we associate two area preserving twist maps: the
(classical) inner billiard in T and the outer billiard in the exterior of T. The invariant circles of …

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane.
BH Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy …

It is shown that a large class of solutions in two-degree-of-freedom Hamiltonian systems of
billiard type can be described by slowly varying one-degree-of-freedom Hamiltonian …

0.1 Introduction These lecture notes describe a new development in the calculus of
variations which is called Aubry-Mather-Theory. The starting point for the theoretical …