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A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere

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Bonino M.

Fundamenta Mathematicae

2004

tom 182

nr 1

1-40

We provide a topological proof that each orientation reversing homeomorphism of the 2-sphere which has a point of period k ≥ 3 also has a point of period 2. Moreover if such a k-periodic point can be chosen arbitrarily close to an isolated fixed point o then the same is true for the 2-periodic point. We also strengthen this result by proving that if an orientation reversing homeomorphism h of the sphere has no 2-periodic point then the complement of the fixed point set can be covered by invariant open sets where h is conjugate either to the map (x,y) ↦ (x+1,-y) or to the map (x,y) ↦ 1/2(x,-y).

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1 Fundamenta Mathematicae

1 Bonino M.

1 2004

Wyniki wyszukiwania

A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere