11 citations · 24 across the 9 of their papers we have counts for
7 papers · 1 filter
Nontrivial paths and periodic orbits of the -fractal billiard table
Michel L. Lapidus, Robyn L. Miller, Robert G. Niemeyer
We introduce and prove numerous new results about the orbits of the -fractal billiard. Specifically, in Section 3, we give a variety of sufficient conditions for the existence o…
Properties of the flow on a polygonal Andreev billiard
Robert G. Niemeyer
A formal definition of a (mathematical) polygonal Andreev billiard and a construction of an equivalence relation that captures the dynamics described in physical toy model of Andre…
Periodic billiard orbits of self-similar Sierpinski carpets
Joe P. Chen, Robert G. Niemeyer
We identify a collection of periodic billiard orbits in a self-similar Sierpinski carpet billiard table. Based on a refinement of the result of Durand-Cartagena and Tyson regarding…
The current state of fractal billiards
Michel L. Lapidus, Robert G. Niemeyer
If D is a rational polygon, then the associated rational billiard table is given by Ω(D). Such a billiard table is well understood. If F is a closed fractal curve approximated by a…
Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards
Michel L. Lapidus, Robert G. Niemeyer
The Koch snowflake KS is a nowhere differentiable curve. The billiard table Omega(KS) with boundary KS is, a priori, not well defined. That is, one cannot a priori determine the mi…
Families of Periodic Orbits of the Koch Snowflake Fractal Billiard
Michel L. Lapidus, Robert G. Niemeyer
We describe the periodic orbits of the prefractal Koch snowflake billiard (the nth inner rational polygonal approximation of the Koch snowflake billiard). In the case of the finite…
Towards the Koch Snowflake Fractal Billiard: Computer Experiments and Mathematical Conjectures
Michel L. Lapidus, Robert G. Niemeyer
In this paper, we attempt to define and understand the orbits of the Koch snowflake fractal billiard . This is a priori a very difficult problem because , the sno…