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Normes sur le groupe des contactomorphismes et contactisation de domaines étoilés, leurs géodésiques et leurs caractéristiques translatées.

Abstract : We study different norms on the group of contactomorphisms of a contact manifold. For every integers n greater than 0, using generating function techniques, we characterise some geodesics of the group of compactly supported contactomorphisms of R2n x S^1 endowed with its standard contact structure. We compute explicitely the norm of a big family of contactomorphisms of the unitary cotangent of the torus using a theorem of  intersections between exact Lagrangians with the 0-section inside the cotangent. Finally we study the characteristic distribution on hypersurfaces lying inside the contactification of an exact symplectic manifold. It allows us to define a new set of values for open domains of the contact manifold considered. This set of values contains contact invariants and generalise the notion of the spectrum of an open domain in an exact symplectic manifold.
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https://tel.archives-ouvertes.fr/tel-03700704
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Submitted on : Tuesday, June 21, 2022 - 1:33:22 PM
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Pierre-Alexandre Arlove. Normes sur le groupe des contactomorphismes et contactisation de domaines étoilés, leurs géodésiques et leurs caractéristiques translatées.. Géométrie différentielle [math.DG]. Université de Strasbourg, 2021. Français. ⟨NNT : 2021STRAD019⟩. ⟨tel-03700704v2⟩

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