It is known that every expansive homeomorphism has finite topological entropy, also expansivity implies sensitivity.
I would like to know that relation between topological entropy and sensitivity. Please help me to know it or introduce a reference for it.
Thanks a lot.
There is none (maybe in some specific setting you could come up with something, but in this generality no). Sensitivity is a global property, but topological entropy is not. For example, you could have a dynamical system with an invariant set $\Lambda$ such that the topological entropy of $f|_{\Lambda}$ is positive (which implies that the entropy of $f$ is positive), but at the same time there is an open set $U$ in your space such that $f|_U$ is the identity (which prevents sensitivity).
In the result you mentioned there is a stronger global property present, expansivity.