Periodic Points on the 2-sphere

TL;DR

This paper proves that a certain class of smooth, degree-two, latitude-preserving maps on the 2-sphere necessarily have an exponential number of periodic points.

Contribution

It establishes a lower bound of 2^n periodic points for these maps, advancing understanding of their dynamical complexity.

Findings

Maps have at least 2^n periodic points.

The result applies to C^1 degree-two latitude-preserving endomorphisms.

Provides a new insight into the periodic structure of such sphere maps.

Abstract

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