TY - JOUR
T1 - Rotation Sets of Billiards with N Obstacles on a Torus
AU - Alsheekhhussain, Zainab
PY - 2019/10/1
Y1 - 2019/10/1
N2 - For billiards with N obstacles on a torus, we study the behavior of specific kind of its trajectories, the so called admissible trajectories. Using the methods developed in Blokh et al. (Commun Math Phys 266:239–265, 2006), we prove that the admissible rotation set is convex, and the periodic trajectories of admissible type are dense in the admissible rotation set. In addition, we show that the admissible rotation set is a proper subset of the general rotation set.
AB - For billiards with N obstacles on a torus, we study the behavior of specific kind of its trajectories, the so called admissible trajectories. Using the methods developed in Blokh et al. (Commun Math Phys 266:239–265, 2006), we prove that the admissible rotation set is convex, and the periodic trajectories of admissible type are dense in the admissible rotation set. In addition, we show that the admissible rotation set is a proper subset of the general rotation set.
KW - Admissible rotation set
KW - General rotation set
KW - Rotation vector
KW - Torus
UR - http://www.scopus.com/inward/record.url?scp=85074847725&partnerID=8YFLogxK
U2 - 10.1007/s12591-015-0269-3
DO - 10.1007/s12591-015-0269-3
M3 - Article
AN - SCOPUS:85074847725
SN - 0971-3514
VL - 27
SP - 369
EP - 377
JO - Differential Equations and Dynamical Systems
JF - Differential Equations and Dynamical Systems
IS - 4
ER -