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

Fundamenta Mathematicae (2004)

- Volume: 182, Issue: 1, page 1-40
- ISSN: 0016-2736

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topMarc Bonino. "A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere." Fundamenta Mathematicae 182.1 (2004): 1-40. <http://eudml.org/doc/283190>.

@article{MarcBonino2004,

abstract = {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).},

author = {Marc Bonino},

journal = {Fundamenta Mathematicae},

keywords = {homeomorphism of the 2-sphere; orientation reversing; periodic point},

language = {eng},

number = {1},

pages = {1-40},

title = {A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere},

url = {http://eudml.org/doc/283190},

volume = {182},

year = {2004},

}

TY - JOUR

AU - Marc Bonino

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

JO - Fundamenta Mathematicae

PY - 2004

VL - 182

IS - 1

SP - 1

EP - 40

AB - 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).

LA - eng

KW - homeomorphism of the 2-sphere; orientation reversing; periodic point

UR - http://eudml.org/doc/283190

ER -

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