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On finite-time hyperbolicity
A note on almost periodic variational equations
1. | Department of Mathematics, University of Sussex, Brighton, BN1 9RF |
2. | Martin Rasmussen, Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom |
In addition, we also discuss this problem in the discrete case by considering the variational equation $x_{n+1}=D_xF(n,\mu_n)x_n$ of the almost periodic difference equation $x_{n+1}=F(n,x_n)$ along an almost periodic solution $\mu_n$. In particular, we provide an example of a function $F$ which is discrete almost periodic uniformly in $x$ and whose derivative $D_xF$ is not discrete almost periodic.
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