Cohomology classes of dynamically non-negative Ck functions |
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| Authors: | Thierry Bousch Oliver Jenkinson |
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| Institution: | (1) Laboratoire de Mathématique (UMR 8628 du CNRS), bat. 425, Université de Paris-Sud, 91405 Orsay Cedex, France (e-mail: Thierry.Bousch@math.u-psud.fr), FR;(2) School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK (e-mail: omj@maths.qmw.ac.uk), GB |
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| Abstract: | Let T:x↦2x (mod 1) be the doubling map of the circle ?=ℝ/ℤ. We construct a trigonometric polynomial f:?→ℝ with the following property: ∫f
dμ≥0 for every T-invariant probability measure μ, so that f is cohomologous to a non-negative Lipschitz function, yet f is not cohomologous to any non-negative C
1 function.
Oblatum 28-VI-2001 & 4-X-2001?Published online: 18 January 2002 |
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