Journal of the
Korean Mathematical Society JKMS

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}=\{f_i\}_{i=1}^{\infty}\;$ on circles is $\;h(f_{1,\infty})=\limsup\limits_{n\rightarrow\infty}\frac{1}{n}\log\prod\limits_ {i=1}^{n}|\deg f_{i}|.$ As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism $f$ on a smooth $2$-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.

Keywords: sequence of continuous maps, topological entropy, separated set, spanning set

MSC numbers: 37B40, 37B55