3 papers
math.DS2010
Homotopical Complexity of 2D Billiard Orbits
Lee M. Goswick, Nandor Simanyi
Traditionally, rotation numbers for toroidal billiard flows are defined as the limiting vectors of average displacements per time on trajectory segments. The billard trajectories,…
math.NT2008
Sums of squares and orthogonal integral vectors
Lee M. Goswick, Emil W. Kiss, Gabor Moussong +1
Two vectors in $\BZ^3$ are called \emph{twins} if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin p…
math.DS2006
Homotopical Rotation Numbers of 2D Billiards
Lee M. Goswick, Nandor Simanyi
Traditionally, rotation numbers for toroidal billiard flows are defined as the limiting vectors of average displacements per time on trajectory segments. Naturally, these creatures…