Multivalued Lyapunov functions for homeomorphisms of the 2-torus

• Autorzy: Patrice Le Calvez
• Języki publikacji: EN

Abstrakty

EN

Let F be a homeomorphism of 𝕋² = ℝ²/ℤ² isotopic to the identity and f a lift to the universal covering space ℝ². We suppose that κ ∈ H¹(𝕋²,ℝ) is a cohomology class which is positive on the rotation set of f. We prove the existence of a smooth Lyapunov function of f whose derivative lifts a non-vanishing smooth closed form on 𝕋² whose cohomology class is κ.

Kategorie tematyczne

• 37E35: Flows on surfaces
• 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
• 37B25: Lyapunov functions and stability; attractors, repellers
• 37E45: Rotation numbers and vectors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 3
• Strony: 227-253

Daty

wydano

2006

Twórcy

autor

Patrice Le Calvez

• Laboratoire Analyse, Géométrie et Applications, C.N.R.S.-U.M.R 7539, Institut Galilée, Université Paris 13, Avenue J.-B. Clément, 93430 Villetaneuse, France

Identyfikatory

DOI

10.4064/fm189-3-2