The aim of this paper is to share with the mathematical community a list of 33 problems that I
have found along the years in my research. I believe that it is worth to think about them and …

Publisher Summary The theory of mathematical billiards can be partitioned into three areas:
convex billiards with smooth boundaries, billiards in polygons (and polyhedra), and …

In this chapter we briefly give the theory (without proofs) of discrete and continuous-time
dynamical systems. This will be helpful for the reader, because a mathematical billiard which …

Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Page 1
Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Richard …

The notions of shadowing, specification and gluing orbit property differ substantially for
discrete and continuous time dynamical systems. In the present paper we continue the study …

Let S ε denote the set of Euclidean triangles whose two small angles are within ε radians of
and respectively. In this paper we prove two complementary theorems:(1) For any ε> 0 there …

We demonstrate the equoivalence of two seemingly disparate dynamical systems. One
consits of three hard rods sliding along a frictionless ring and making elastic collisions. The …

Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable
evolution and sudden jumps due to conical singular points that arise from the corners of the …

Рассмотрена проблема периодичности, т. е. существования апериодической точки и
полноты меры периодических точек для внешних биллиардов вне правильных n …

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic
billiard path. Our proof involves the analysis of certain infinite families of Fourier series that …