Multivalued Lyapunov functions for homeomorphisms of the
2-torus
Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 227-253
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $F$ 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
$\kappa$.
Keywords:
homeomorphism mathbb mathbb mathbb isotopic identity lift universal covering space mathbb suppose kappa mathbb mathbb cohomology class which positive rotation set prove existence smooth lyapunov function whose derivative lifts non vanishing smooth closed form mathbb whose cohomology class kappa
Affiliations des auteurs :
Patrice Le Calvez 1
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author = {Patrice Le Calvez},
title = {Multivalued {Lyapunov} functions for homeomorphisms of the
2-torus},
journal = {Fundamenta Mathematicae},
pages = {227--253},
publisher = {mathdoc},
volume = {189},
number = {3},
year = {2006},
doi = {10.4064/fm189-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-2/}
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TY - JOUR AU - Patrice Le Calvez TI - Multivalued Lyapunov functions for homeomorphisms of the 2-torus JO - Fundamenta Mathematicae PY - 2006 SP - 227 EP - 253 VL - 189 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-2/ DO - 10.4064/fm189-3-2 LA - en ID - 10_4064_fm189_3_2 ER -
Patrice Le Calvez. Multivalued Lyapunov functions for homeomorphisms of the 2-torus. Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 227-253. doi: 10.4064/fm189-3-2
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