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The Stability of the Equilibrium of Planar Hamiltonian and Reversible Systems

Authors:

Bin Liu

Affiliation:

(1) LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R.China

Abstract:

In this paper, we study the stability of the equilibrium of planar systems

$$x^prime = X(x,y,t), quad y^prime = Y(x,y,t),$$

where X and Y are real analytic in x, y, and t, and quasi-periodic in t with frequencies (ω₁,...,ω_n). Under some reasonable assumptions, we obtain a sufficient and necessary condition.

Keywords:

Stability of the equilibrium Hamiltonian systems reversible systems quasi-periodic functions invariant curves

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