scholarly journals A locally integrable multi-dimensional billiard system

2017 ◽  
Vol 37 (10) ◽  
pp. 5271-5284 ◽  
Author(s):  
Dmitry Treschev ◽  
Keyword(s):  

1993 ◽  
Vol 26 (20) ◽  
pp. 5365-5373 ◽  
Author(s):  
T Prosen ◽  
M Robnik
Keyword(s):  


2006 ◽  
Vol 73 (3) ◽  
Author(s):  
B. Dietz ◽  
A. Heine ◽  
A. Richter ◽  
O. Bohigas ◽  
P. Leboeuf






2001 ◽  
Vol 34 (12) ◽  
pp. 2561-2569 ◽  
Author(s):  
Der-San Chuu ◽  
De-Hone Lin


2011 ◽  
Vol 182 (1) ◽  
pp. 245-248 ◽  
Author(s):  
Mitsuyoshi Tomiya ◽  
Hiroyoshi Tsuyuki ◽  
Shoichi Sakamoto


2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Theresa S. Bonenberger ◽  
Jörg Baumgart ◽  
Cornelius Neumann

AbstractFor mixing light from different colored LEDs, an optical color mixing system is required to avoid colored shadows and color fringes. Concerning the different color mixing systems, mixing rods are widespread as they provide very good spatial color mixing with high efficiency. The essential disadvantage of mixing rods, so far, is the lack of angular color mixing. The solution presented in this publication is the application of a chaotic-dispersive billiard’s geometry on the cross section of the mixing rod. To show both the spatial and the angular mixing properties of a square and a chaotic-dispersive mixing rod, simulations generated by the raytracing software ASAP are provided. All results are validated with prototype measurements.





2000 ◽  
Vol 07 (01n02) ◽  
pp. 151-160
Author(s):  
R. W. ROBINETT

We present a periodic orbit theory analysis of a novel three-dimensional billiard system, namely a quasispherical cavity with infinite walls along the conical boundary defined by θ=Θ, where θ is the standard polar angle; for Θ=π/2 this reduces to the special case of a hemispherical infinite well, while for Θ=π it is a spherical well with points along the negative z axis excluded. We focus especially on the connections between subsets of the energy eigenvalue space and their contributions to qualitatively different classes of closed orbits.



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