scholarly journals On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Dongfeng Zhang ◽  
Rong Cheng
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems

Homoclinic orbits for invariant tori of nearly integrable Hamiltonian systems

2006 ◽  
Vol 73 (2) ◽  
pp. 217-220
Author(s):  
O. Yu. Koltsova ◽  
L. M. Lerman ◽  
A. Delshams ◽  
P. Gutiérrez
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Homoclinic Orbits ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems

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.

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