- 95-213 Howard Weiss
- A REMARK ON PAPERS BY PIXTON AND OLIVEIRA: GENERICITY OF SYMPLECTIC DIFFEOMORPHISMS OF
$S^2$ WITH POSITIVE TOPOLOGICAL ENTROPY
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May 8, 95
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Abstract. We prove the existence of an open and dense subset of maps $ f \in Diff^{\infty}_{\omega}(S^2)$
which have positive topological entropy. It follows that these maps have infinitely many
hyperbolic periodic points and an exponential growth rate of hyperbolic periodic points.
The proof is an application of Pixton's theorem.
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