Multivalued Lyapunov functions for homeomorphisms of the 2-torus
Fundamenta Mathematicae (2006)
- Volume: 189, Issue: 3, page 227-253
- ISSN: 0016-2736
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topPatrice Le Calvez. "Multivalued Lyapunov functions for homeomorphisms of the 2-torus." Fundamenta Mathematicae 189.3 (2006): 227-253. <http://eudml.org/doc/283017>.
@article{PatriceLeCalvez2006,
abstract = {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.},
author = {Patrice Le Calvez},
journal = {Fundamenta Mathematicae},
keywords = {homeomorphism of the torus; foliation; rotation vector; rotation set; brick decomposition},
language = {eng},
number = {3},
pages = {227-253},
title = {Multivalued Lyapunov functions for homeomorphisms of the 2-torus},
url = {http://eudml.org/doc/283017},
volume = {189},
year = {2006},
}
TY - JOUR
AU - Patrice Le Calvez
TI - Multivalued Lyapunov functions for homeomorphisms of the 2-torus
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 3
SP - 227
EP - 253
AB - 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.
LA - eng
KW - homeomorphism of the torus; foliation; rotation vector; rotation set; brick decomposition
UR - http://eudml.org/doc/283017
ER -
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