scholarly journals Quantum revivals in two degrees of freedom integrable systems: The torus case

2012 ◽  
Vol 77 (1-2) ◽  
pp. 1-41
Author(s):  
Olivier Lablée
Keyword(s):  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Two Degrees Of Freedom ◽  
Quantum Revivals

scholarly journals The reduction of the degree of integrals of hamiltonian systems with the help of billiards

2019 ◽  
Vol 486 (2) ◽  
pp. 151-155
Author(s):  
V. V. Vedyushkina ◽  
A. T. Fomenko
Keyword(s):  
Lie Algebra ◽  
Hamiltonian Systems ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Quadratic Integral ◽  
High Degree

In the theory of integrable Hamiltonian systems with two degrees of freedom there are widely known integrable systems whose integrals have a high degree, namely 3 and 4: the Kovalevskaya system and its generalizations - the Kovalevskaya - Yahya system and the Kovalevskaya system on the Lie algebra so(4), Goryachev-Chaplygin-Sretensky, Sokolov and Dullin-Matveyev. The article shows that using integrable billiards bounded by arcs of confocal quadrics decreases the degree of integrals 3 and 4 of these systems fo some isoenergy 3-surfaces. Moreover, the integrals of degree 3 and 4 reduce to the same canonical quadratic integral on billiards.

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