Chaos in almost periodic systems (Q912453)

Let \(dx/dt=f(t,x)\) be an almost periodic differential equation with a hyperbolic almost periodical solution u(t) and another hyperbolic solution v(t) satisfying \(| v(t)-u(t)| \to 0\) as \(| t| \to \infty\). The authors prove that the solutions of such an equation exhibit chaotic behavior. This result extends the known results when f(t,x) is either periodic or an almost periodically perturbation: \(f(t,x)=g(x)+\epsilon h(t,x,\epsilon).\)