Abstract
We consider the rotation setR of a homeomorphismf, isotopic to the identity, of a closed surface Σ of genusg≤2. We show if Int(R) is nonempty and contains an element which is realized by an asymptotic measure, then all the rational points of Int(R) are realized by periodic orbits. We raise an example to show that the second condition above is indispensable ifg≥2. We also show that ifR contains a (g+1)-simplex whose vertices are realizable by periodic orbits, then the topological entropy off is positive.
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