F. Hertz

Entropy and semiconjugacy on surfaces

Let $g$ be a $C^\infty$ diffeomorphism in the isotopy class of a pseudo-Anosov homeomorphism $f$ such that $g$ and $f$ have the same topological entropy. In 1988, Handel proved that this implies the existence of a semiconjugacy $\pi$ from $g$ to $f$. He stated that, in general, there is at least one point $x$ such that...