Multivalued Lyapunov functions for homeomorphisms of the 2-torus
Volume 189 / 2006
Fundamenta Mathematicae 189 (2006), 227-253
MSC: 37B25, 37E30, 37E35, 37E45.
DOI: 10.4064/fm189-3-2
Abstract
Let be a homeomorphism of \mathbb T^2=\mathbb R^2/\mathbb Z^2 isotopic to the identity and f a lift to the universal covering space \mathbb R^2. We suppose that \kappa\in H^1(\mathbb T^2,\mathbb 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 \mathbb T^2 whose cohomology class is \kappa.
