Generalized-periodic motions of nonautonomous systems
Let \((\Sigma,d)\) be a metric space. The authors call a continuous mapping \[ f(\tau,t,x)=G(\tau,t)x:{\mathbb R}\times{\mathbb R}^+\times\Sigma \to\Sigma \] a motion if \(G(\tau,0)x=x\) and there exists a \(T>0\) such that \[ G(\tau+T,t)G(\tau,T)=G(\tau,t+T). \] A motion \(f\) is called generalized periodic if for any \(\epsilon>0\) there exists a positive integer \(N_{\epsilon}\) such that \[ d(f(\tau,t,x),f(\tau,t+N_{\epsilon}T,x))<\epsilon \] for all \(t\in{\mathbb R}^+\). The authors study relations between integral invariant sets and generalized periodic motions.
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