scholarly journals Integrable Hamiltonian Systems with a Periodic Orbit or Invariant Torus Unique in the Whole Phase Space

2018 ◽  
Vol 4 (3-4) ◽  
pp. 415-422 ◽  
Author(s):  
Mikhail B. Sevryuk
Keyword(s):  
Phase Space ◽  
Periodic Orbit ◽  
Hamiltonian Systems ◽  
Invariant Torus ◽  
Integrable Hamiltonian Systems

Canonical Transformations, Entropy and Quantization

1987 ◽  
Vol 42 (4) ◽  
pp. 333-340 ◽  
Author(s):  
B. Bruhn
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Arbitrary Function ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Integrable Hamiltonian Systems ◽  
Eigenvalue Spectrum ◽  
Complex Phase ◽  
Algebraic Treatment ◽  
Canonical Coordinate

This paper considers various aspects of the canonical coordinate transformations in a complex phase space. The main result is given by two theorems which describe two special families of mappings between integrable Hamiltonian systems. The generating function of these transformations is determined by the entropy and a second arbitrary function which we take to be the energy function. For simple integrable systems an algebraic treatment based on the group properties of the canonical transformations is given to calculate the eigenvalue spectrum of the energy.

On Invariant Tori with Prescribed Frequency in Hamiltonian Systems

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Dongfeng Zhang ◽  
Junxiang Xu ◽  
Hao Wu
Keyword(s):  
Hamiltonian Systems ◽  
Small Perturbation ◽  
Topological Degree ◽  
Invariant Torus ◽  
Invariant Tori ◽  
Rational Approximations ◽  
Integrable Hamiltonian Systems ◽  
Resonant Condition ◽  
Degeneracy Condition ◽  
Nearly Integrable Hamiltonian Systems

AbstractIn this paper we are mainly concerned with the persistence of invariant tori with prescribed frequency for analytic nearly integrable Hamiltonian systems under the Brjuno–Rüssmann non-resonant condition, when the Kolmogorov non-degeneracy condition is violated. As it is well known, the frequency of the persisting invariant tori may undergo some drifts, when the Kolmogorov non-degeneracy condition is violated. By the method of introducing external parameters and rational approximations, we prove that if the Brouwer topological degree of the frequency mapping is nonzero at some Brjuno–Rüssmann frequency, then the invariant torus with this frequency persists under small perturbation.

scholarly journals Two-Photon Algebra and Integrable Hamiltonian Systems

2001 ◽  
Vol 8 (sup1) ◽  
pp. 18-22 ◽  
Author(s):  
Angel Ballesteros ◽  
Francisco J Herranz
Keyword(s):  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Two Photon
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