Eine bemerkung zur topologischen entropie

We study fractional quadratic transformations T of the sphere and try to determine their topological entropy. In the case where T is a constant mapping or a homeomorphism, the topological entropy is of course zero. In the other cases, we have the following results. If T has only one fixed point, its entropy is log 2. If T has exactly two fixed points, it can be written as T_z=z-z^-1+v, and if v is real, then the entropy of T is again log 2. A general result of Misiurewicz and Przytycki shows that the entropy of T is at least log2, and we conjecture that this entropy is always equal to log2 in the remaining cases, i. e. two fixed points and v not real, and three fixed points.