Methods for determination and approximation of the domain of attraction in the case of autonomous discrete dynamical systems.
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Multivalued Lyapunov functions for homeomorphisms of the 2-torus
Patrice Le Calvez (2006)
Fundamenta Mathematicae
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.
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