Periodic points on the $2$-sphere

Charles Pugh; Michael Shub

doi:10.3934/dcds.2014.34.1171

Article Contents

2014, Volume 34, Issue 3: 1171-1182. Doi: 10.3934/dcds.2014.34.1171

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Periodic points on the $2$-sphere

Charles Pugh^1, and
Michael Shub^2,

1.
Department of Mathematics, University of Chicago, 5734 S. University Ave, Chicago, Illinois 60637
2.
CONICET, IMAS, Universidad de Buenos Aires, Buenos Aires

Received: September 30, 2012

Revised: February 28, 2013

Published: February 2014

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Abstract

For a $C^{1}$ degree two latitude preserving endomorphism $f$ of the $2$-sphere, we show that for each $n$, $f$ has at least $2^{n}$ periodic points of period $n$.

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Mathematics Subject Classification: Primary: 37C25.

Citation:

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References

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