  We dedicate this paper to the topological analysis of subwavelength solutions
in Floquet metamaterials. This work should be considered as a basis for further
investigation on whether topological properties of the bulk materials are
linked to the occurrence of edge modes. The subwavelength solutions being
described by a periodically parameterized time-periodic linear ordinary
differential equation $\left\{\frac{d}{dt}X = A_\alpha(t)X\right\}_{\alpha \in
\mathbb{T}^d}$, we put ourselves in the general setting of periodically
parameterized time-periodic linear ordinary differential equations and
introduce a way to (topologically) classify a Floquet normal form $F,~P$ of the
associated fundamental solution $\left\{X_\alpha(t) =
P(\alpha,t)\exp(tF_\alpha)\right\}_{\alpha \in \mathbb{T}^d}$. This is achieved
by analysing the topological properties of the eigenvalues and eigenvectors of
the monodromy matrix $X_\alpha(T)$ and the Lyapunov transformation
$P(\alpha,t)$. The corresponding topological invariants can then be applied to
the setting of Floquet metamaterials. In this paper these general results are
considered in the case of honeycomb Floquet metamaterials. We provide two
interesting examples of topologically non-trivial time-modulated honeycomb
structures.
