  In this paper, we give an example of an autoequivalence with positive
categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and
Kontsevich) for any surface containing a (-2)-curve. Then we show that this
equivalence gives another counter-example to a conjecture proposed by Kikuta
and Takahashi. In a second part, we study the action on cohomology induced by
spherical twists composed with standard autoequivalences on a surface S and
show that their spectral radii correspond to the topological entropy of the
corresponding automorphisms of S.
