Quasi-periodic bifurcations in reversible systems

2010 ◽  
Vol 16 (1-2) ◽  
pp. 51-60 ◽  
Author(s):  
Heinz Hanßmann
Keyword(s):  
Reversible Systems

Determination of stability constants of quasi-reversible systems

1983 ◽  
Vol 143 (1-2) ◽  
pp. 397-411 ◽  
Author(s):  
M.L.S. Simões Gonçalves ◽  
M.M. Correia Dos Santos
Keyword(s):  
Stability Constants ◽  
Reversible Systems

scholarly journals Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

2006 ◽  
Vol 214 (2) ◽  
pp. 169-181 ◽  
Author(s):  
Kazuyuki Yagasaki ◽  
Thomas Wagenknecht
Keyword(s):  
Homoclinic Orbits ◽  
Reversible Systems

scholarly journals The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yanling Shi ◽  
Jia Li
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Order Differential Equation ◽  
Reversible Systems ◽  
Invariant Curves ◽  
Real Analytic Functions ◽  
All Solutions ◽  
Small Twist Theorem ◽  
Real Analytic ◽  
Twist Theorem

We study the following two-order differential equation,(Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0,whereΦp(s)=|s|(p-2)s,p>0.f(x,t)andg(x,t)are real analytic functions inxandt,2aπp-periodic inx, and quasi-periodic intwith frequencies(ω1,…,ωm). Under some odd-even property off(x,t)andg(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense ofsupt∈R|x′(t)|<+∞.

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