Exponentially Small Splitting in Hamiltonian Systems

1994 ◽  
pp. 181-187
Author(s):  
Amadeu Delshams ◽  
Tere M. Seara
Keyword(s):  
Hamiltonian Systems ◽  
Exponentially Small Splitting ◽  
Exponentially Small

scholarly journals Exponentially small splitting for whiskered tori in Hamiltonian systems: flow-box coordinates and upper bounds

2004 ◽  
Vol 11 (4) ◽  
pp. 785-826 ◽  
Author(s):  
Amadeu Delshams ◽  
◽  
Pere Gutiérrez ◽  
Tere M. Seara ◽  
◽  
...  
Keyword(s):  
Hamiltonian Systems ◽  
Upper Bounds ◽  
Exponentially Small Splitting ◽  
Whiskered Tori ◽  
Exponentially Small

scholarly journals On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Nina Xue ◽  
Wencai Zhao
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Linear Hamiltonian System ◽  
Constant Matrix ◽  
Change Of Variables ◽  
Periodic Linear ◽  
Multiple Eigenvalues ◽  
Linear Hamiltonian Systems ◽  
Constant Coefficients ◽  
Exponentially Small

In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q.

Exponentially small splittings in Hamiltonian systems

1991 ◽  
Vol 1 (2) ◽  
pp. 137-142 ◽  
Author(s):  
V. G. Gelfreich ◽  
V. F. Lazutkin ◽  
M. B. Tabanov
Keyword(s):  
Hamiltonian Systems ◽  
Exponentially Small
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