Invariant tori for semilinear reversible systems

2004 ◽  
Vol 56 (1) ◽  
pp. 133-146 ◽  
Author(s):  
Xiong Li
Keyword(s):  
Invariant Tori ◽  
Reversible Systems

scholarly journals THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION

2007 ◽  
Vol 17 (08) ◽  
pp. 2605-2623 ◽  
Author(s):  
HENK W. BROER ◽  
M. CRISTINA CIOCCI ◽  
HEINZ HANßMANN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Invariant Tori ◽  
Kam Theory ◽  
Cantor Sets ◽  
Reversible Systems ◽  
Periodic Dynamics

We consider the perturbed quasi-periodic dynamics of a family of reversible systems with normally 1:1 resonant invariant tori. We focus on the generic quasi-periodic reversible Hopf bifurcation and address the persistence problem for integrable quasi-periodic tori near the bifurcation point. Using KAM theory, we describe how the resulting invariant tori of maximal and lower dimensions are parameterized by Cantor sets.

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