Isochronous centers of cubic reversible systems

2008 ◽  
pp. 255-268 ◽  
Author(s):  
Javier Chavarriga ◽  
Isaac García
Keyword(s):  
Reversible Systems ◽  
Isochronous Centers

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

Quasi-periodic bifurcations in reversible systems

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

BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM

2013 ◽  
Vol 23 (10) ◽  
pp. 1350172 ◽  
Author(s):  
WENTAO HUANG ◽  
AIYONG CHEN ◽  
QIUJIN XU
Keyword(s):  
Limit Cycles ◽  
Necessary Conditions ◽  
Polynomial System ◽  
Isochronous Center ◽  
Eighth Order ◽  
Bifurcation Of Limit Cycles ◽  
Quartic Polynomial ◽  
Fine Focus ◽  
Sufficient And Necessary Conditions ◽  
Isochronous Centers

For a quartic polynomial system we investigate bifurcations of limit cycles and obtain conditions for the origin to be a center. Computing the singular point values we find also the conditions for the origin to be the eighth order fine focus. It is proven that the system can have eight small amplitude limit cycles in a neighborhood of the origin. To the best of our knowledge, this is the first example of a quartic system with eight limit cycles bifurcated from a fine focus. We also give the sufficient and necessary conditions for the origin to be an isochronous center.

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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