Journal of the
Korean Mathematical Society JKMS

For a switched system with constraint on switching sequences, which is also called a subshift action, on a metric space not necessarily compact, two kinds of topological entropies, average topological entropy and maximal topological entropy, are introduced. Then we give some properties of those topological entropies and estimate the bounds of them for some special systems, such as subshift actions generated by finite smooth maps on $p$-dimensional Riemannian manifold and by a family of surjective endomorphisms on a compact metrizable group. In particular, for linear switched systems on $\mathbb R^p$, we obtain a better upper bound, by joint spectral radius, which is sharper than that by Wang et al. in \cite{Wang-Ma2015, Wang-Ma-Lin2016}.

Keywords: maximal topological entropy, average topological entropy, switched system, joint spectral radius

MSC numbers: 37A35, 37B10, 37B40, 37B55