scholarly journals Violation of adiabaticity in magnetic billiards due to separatrix crossings

2015 ◽  
Vol 25 (8) ◽  
pp. 083109 ◽  
Author(s):  
A. V. Artemyev ◽  
A. I. Neishtadt
Keyword(s):  
Magnetic Billiards

scholarly journals Algebraic non-integrability of magnetic billiards

2016 ◽  
Vol 49 (45) ◽  
pp. 455101 ◽  
Author(s):  
Misha Bialy ◽  
Andrey E Mironov
Keyword(s):  
Magnetic Billiards

scholarly journals A survey on polynomial in momenta integrals for billiard problems

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170418 ◽  
Author(s):  
Misha Bialy ◽  
Andrey E. Mironov
Keyword(s):  
Constant Curvature ◽  
Integrable Systems ◽  
Theme Issue ◽  
Algebraic Version ◽  
Finite Dimensional ◽  
Short Survey ◽  
Magnetic Billiards ◽  
Algebraic Technique

In this paper, we give a short survey of recent results on the algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique, we study the existence of polynomial integrals for the two-sided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

The Exterior and Interior Edge States of Magnetic Billiards: Spectral Statistics and Correlations

2001 ◽  
Vol T90 (1) ◽  
pp. 64 ◽  
Author(s):  
Klaus Hornberger ◽  
Klaus Hornberger ◽  
Uzy Smilansky
Keyword(s):  
Edge States ◽  
Interior Edge ◽  
Spectral Statistics ◽  
Magnetic Billiards
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