Lyapunov Exponents of Certain 1D Sensitive Open CA with a Continuum of δ−Periodic Points

Let A^Z be a metric Cantor space of bi-infinite words and (A^Z, σ) its corresponding full shift. Consider surjective CA (A^Z, F), (A^Z, σ) with the Borel uniform Bernoulli measure μ. Let h_μ (A^Z, F) and h_μ (A^Z, σ) denote KS-entropies of suitable CA. Denote by h(A^Z, F) the topological entropy of (A^Z, F). It is a well-known fact that for the former(Formul presented) Lyapunov exponents of (A^Z, F), the inequalities (Formul presented) hold. Furthermore, under the above assumptions, there are examples of (A^Z, F) such that the average Lyapunov exponents provide a better upper bound for h_μ (A^Z, F) than the former ones [P. Tisseur, Nonlin-earity 13 (2000)]. In this paper we prove that under somewhat stronger assumptions, the average and former Lyapunov exponents can provide at least as excessive a real upper bound for h_μ (A^Z, F) and h(A^Z, F), respectively, as we choose it to be.