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Invariants analytiques des difféomorphismes et multizêtas

Abstract : This work contains two independant parts, witch are deeply very closed. The first part deals with the calculation and the numerical evaluation of the holomor¬phic invariants of tangent to identity diffeomorphisms, in the type-case. ln particular, we display here three methods of numerical computation whose the last is based on an ex¬plicit formula of invariants. These result of calculation of the horn map 7[+, whose basics components are sorne rationnaIs, sorne Taylor coefficients of the diffeomorphism which is studied and multitangents. The second part deals with a général study of multitangents and relations between them. They are I-periodic functions, generalizing Eisenstein series and defining a symetr~l mould. There are others relations, like the reduction into monotangents which point out to us a profound link between multitangents and multiz~tas values. Properties and conjec¬tures of purely algebraic, arithmetical or analytical kirig are then explain
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Olivier Bouillot. Invariants analytiques des difféomorphismes et multizêtas. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112224⟩. ⟨tel-00647909⟩



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