N ov 2 00 6 APPROXIMATION AND BILLIARDS
نویسنده
چکیده
This survey is based on a series of talks I gave at the conference " Dynamical systems and diophantine approximation " at l'Instut Henri Poincaré in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundance of periodic trajectories in certain irrational polygons .
منابع مشابه
1 9 N ov 2 00 7 APPROXIMATION AND BILLIARDS
This survey is based on a series of talks I gave at the conference " Dynamical systems and Diophantine approximation " at l'Instut Henri Poincaré in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundanc...
متن کاملPeriodic orbits contribution to the 2 - point correlation form factor for pseudo - integrable systems
The 2-point correlation form factor, K 2 (τ), for small values of τ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal approximation. The following cases are considered: (i) plane billiards in the form of right triangles with one angle π/n and (ii) rectangular billiards with the Aharono...
متن کامل2 3 Ju l 2 00 1 Bifurcations in One Degree - of - Vibration Quantum Billiards
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also consider the global bifurcation structure. Using a double-well potential as a representative example, we demonstrate how to locate bifurcations in parameter space...
متن کاملApproximation and Billiards
This survey is based on a series of talks I gave at the conference “Dynamical systems and diophantine approximation” at l’Instut Henri Poincaré in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundance ...
متن کاملApproximating multi-dimensional Hamiltonian flows by billiards
The behavior of a point particle traveling with a constant speed in a region D ∈ RN , undergoing elastic collisions at the regions’s boundary, is known as the billiard problem. Various billiard models serve as approximation to the classical and semi-classical motion in systems with steep potentials (e.g. for studying classical molecular dynamics, cold atom’s motion in dark optical traps and mic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006