Problem 113

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For a rational function $f(z)$ giving a degree $n$ map $z \mapsto f(z)$ of $\mathbb S^2$, does this map have entropy $\log n?$

($\ge$ by Misurewicz and = a.e. by Guckenheimer)

Tags

Tags:

Yes, [1]

References

1. [gromov2003entropy] Gromov M\"ıl.  2003.  Enseign. Math. 49:217–235.