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

• Autorzy: Marc Bonino
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 37Bxx: Topological dynamics
• 37C25: Fixed points, periodic points, fixed-point index theory
• 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 1
• Strony: 1-40

Daty

wydano

2004

Twórcy

autor

Marc Bonino

• Institut Galilée, Département de Mathématiques, Université Paris 13, Avenue J.B. Clément, 93430 Villetaneuse, France

Identyfikatory

DOI

10.4064/fm182-1-1