Symplectic capacity and short periodic billiard trajectory
نویسندگان
چکیده
منابع مشابه
Periodic Orbits in Outer Billiard
It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided the boundary is not a parallelogram.
متن کاملPeriodic Billiard Trajectories in Polyhedra
We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a periodic orbit of length four (generalization of Fagnano’s orbit for triangles), moreover we can study completely the orbit of points along this coding.
متن کاملRecurrence and Periodic Billiard Orbits in Polygons
We show that almost all billiard trajectories return parallel to themselves for rank 1, ergodic polygons. Applications are given to the existence of periodic trajectories.
متن کاملPeriodic Billiard Orbits in Right Triangles Ii
Periodic billiard orbits are dense in the phase space of an irrational right triangle. A stronger pointwise density result is also proven.
متن کاملPeriodic billiard orbits in right triangles
There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2012
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-012-0987-y