scholarly journals Fractional Lindstedt series

2006 ◽  
Vol 47 (1) ◽  
pp. 012702 ◽  
Author(s):  
G. Gallavotti ◽  
G. Gentile ◽  
A. Giuliani
Keyword(s):  
Lindstedt Series

A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems

1999 ◽  
Vol 40 (12) ◽  
pp. 6430-6472 ◽  
Author(s):  
G. Gallavotti ◽  
G. Gentile ◽  
V. Mastropietro
Keyword(s):  
Field Theory ◽  
Time Scales ◽  
Theory Approach ◽  
Lindstedt Series

Shape of analyticity domains of Lindstedt series:  The standard map

2001 ◽  
Vol 64 (1) ◽  
Author(s):  
Alberto Berretti ◽  
Corrado Falcolini ◽  
Guido Gentile
Keyword(s):  
Standard Map ◽  
Lindstedt Series

scholarly journals Borel Summability and Lindstedt Series

2006 ◽  
Vol 269 (1) ◽  
pp. 175-193 ◽  
Author(s):  
O. Costin ◽  
G. Gallavotti ◽  
G. Gentile ◽  
A. Giuliani
Keyword(s):  
Borel Summability ◽  
Lindstedt Series

scholarly journals Lindstedt series solutions of the Fermi-Pasta-Ulam lattice

2007 ◽  
Vol 48 (5) ◽  
pp. 052702
Author(s):  
David C. Dooling ◽  
James E. Hammerberg
Keyword(s):  
Series Solutions ◽  
Lindstedt Series

scholarly journals KAM Theory in Configuration Space and Cancellations in the Lindstedt Series

2010 ◽  
Vol 302 (2) ◽  
pp. 359-402 ◽  
Author(s):  
Livia Corsi ◽  
Guido Gentile ◽  
Michela Procesi
Keyword(s):  
Configuration Space ◽  
Kam Theory ◽  
Lindstedt Series

SYNCHRONOUS/ASYNCHRONOUS PATTERNS IN THREE-CELL NETWORKS WITH MULTIPLE TIME DELAYS

2011 ◽  
Vol 21 (06) ◽  
pp. 1701-1718
Author(s):  
YUAN YUAN ◽  
LEI LI
Keyword(s):  
Time Delays ◽  
Fredholm Alternative ◽  
Alternative Theory ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Lindstedt Series ◽  
Leading Term ◽  
Coupled Cell Systems ◽  
The Stability ◽  
Cell Networks

Some patterns of synchrony/asynchrony in the dynamics of coupled cell systems can be predicted by symmetry. However, in the system without symmetry, the different patterns of periodic solutions may exist as well. We consider a general model including three cells with multiple time delays that connect in any possible manner. Our approach is based on the analytic construction by using a perturbation procedure together with the Fredholm alternative theory. Then we employ the Poincaré–Lindstedt series expansion to compute the Floquet exponents which determine the stability. Finally, we resort to numerical computation to get some insights about the leading term in the Floquet exponents, and the numerical simulations are given to confirm the theoretical results.

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