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Equation cohomologique d'un automorphisme affine hyperbolique du tore

Abstract : We study the discrete cohomological equation of a hyperbolic affine automorphism Y of the torus (whose linear part is not necessarily diagonalisable). More precisely ; if d is the cobord operator defined by : d (h) = h-hoY for every element h of the Fréchet space E of the differentiable functions on the torus, we show that the image Im(d) is a closed of E and that consequently the space of cohomology H^1(Y; E):=E/Im(d) is a nontrivial Fréchet space. We also prove the existence of a continuous linear operator L defined from Im(d) to E such that for every element g of Im(d), the image f = L(g) is a solution of the discrete cohomological equation f-foY = g.
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https://hal-uphf.archives-ouvertes.fr/hal-03186400
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Wednesday, March 31, 2021 - 9:44:25 AM
Last modification on : Saturday, October 9, 2021 - 3:21:35 AM

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  • HAL Id : hal-03186400, version 1

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Abdellatif Zeggar. Equation cohomologique d'un automorphisme affine hyperbolique du tore. 2021. ⟨hal-03186400⟩

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