scholarly journals Normal form and Nekhoroshev stability for nearly integrable hamiltonian systems with unconditionally slow aperiodic time dependence

2014 ◽  
Vol 19 (3) ◽  
pp. 363-373 ◽  
Author(s):  
Alessandro Fortunati ◽  
Stephen Wiggins
Keyword(s):  
Normal Form ◽  
Time Dependence ◽  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems ◽  
Nekhoroshev Stability

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>

scholarly journals Normal form analysis of integrable Hamiltonian systems

1991 ◽  
Vol 153 (2-3) ◽  
pp. 101-104 ◽  
Author(s):  
R.C. Miranda Filho ◽  
R.F.S. Andrade
Keyword(s):  
Normal Form ◽  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Form Analysis
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