Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter

Nonlinearity ◽  
2021 ◽  
Vol 34 (12) ◽  
pp. 8192-8247
Author(s):  
Junxiang Xu
Keyword(s):  
Small Parameter ◽  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Lower Dimensional

scholarly journals Normal form for lower dimensional elliptic tori in Hamiltonian systems

2021 ◽  
Vol 4 (6) ◽  
pp. 1-40
Author(s):  
Chiara Caracciolo ◽  
Keyword(s):  
Normal Form ◽  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Integrable Hamiltonian Systems ◽  
Convergence Of An Algorithm ◽  
Planetary Problem ◽  
Order Of Magnitude ◽  
Nearly Integrable Hamiltonian Systems ◽  
Transverse Oscillations ◽  
Lower Dimensional

<abstract><p>We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable normal form. In particular, we adapt the procedure described in a previous work by Giorgilli and co-workers, where the construction was made so as to be used in the context of the planetary problem. We extend the proof of the convergence to the cases in which the two sets of frequencies, describing the motion along the torus and the transverse oscillations, have the same order of magnitude.</p></abstract>

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