On the Persistence of Lower-Dimensional Tori in Reversible Systems with Hyperbolic-Type Degenerate Equilibrium Point Under Small Perturbations

2021 ◽  
Vol 173 (1) ◽  
Author(s):  
Xiaocai Wang ◽  
Xiaofei Cao
Keyword(s):  
Equilibrium Point ◽  
Hyperbolic Type ◽  
Reversible Systems ◽  
Small Perturbations ◽  
Degenerate Equilibrium ◽  
Lower Dimensional Tori ◽  
Lower Dimensional

On the persistence of degenerate lower-dimensional tori in reversible systems

2014 ◽  
Vol 35 (7) ◽  
pp. 2311-2333 ◽  
Author(s):  
XIAOCAI WANG ◽  
JUNXIANG XU ◽  
DONGFENG ZHANG
Keyword(s):  
Differential Equation ◽  
Invariant Torus ◽  
Special Structure ◽  
Reversible Systems ◽  
Small Perturbations ◽  
Normal Matrices ◽  
Lower Dimensional Tori ◽  
Lower Dimensional

This work focuses on the persistence of lower-dimensional tori with prescribed frequencies and singular normal matrices in reversible systems. By the Kolmogorov–Arnold–Moser theory and the special structure of unperturbed nonlinear terms in the differential equation, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [Degenerate lower dimensional tori in reversible systems. J. Math. Anal. Appl.387 (2012), 776–790].

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