Quasi-Periodic Motions in Families of Dynamical Systems by Broer H. W., Huitema G. B.

By Broer H. W., Huitema G. B.

This publication is on Kolmogorov-Arnol'd-Moser concept for quasi-periodic tori in dynamical platforms. It provides an up to date file at the position parameters play for persis- tence of such tori, commonly occuring on Cantor units of confident Hausdorff degree within section and parameter area. The situations with renovation of symplectic or quantity types or time-reversal symmetries are incorporated. The options of Whitney-smoothness and Diophantine approximation of Cantor units on submanifolds of Euclidean area are handled, in addition to Bruno's conception on analytic continuation of tori. partially this fabric is new to Western mathematicians. The reader will be conversant in dynamical platforms thought, differen- tial equations and a few research. The booklet is directed to researchers, yet its front point is introductory.

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Plus loin, signalons la formulation équivalente de (22), obtenue logarithmes des deux membres, et en égalant les coefficients l’endomorphisme de Hi1(X , F) défini par le frobenius "absolu". Nous inspirant de WEIL, cette formule peut être interprétée comme une formule "purement géométrique", du type de Lefschetz, portant sur X et le faisceau induit F sur X . Pour ceci, remarquons que si fX est l’endomorphisme de Frobenius de X, alors pour tout faisceau étale F sur X, on a un isomorphisme canonique où fi d’où De en est prenant l’image inverse sur X , fait, ce "opère" sur la un isomorphisme canonique H1(~ , F) , cohomologie i.

Spring 1962. - [2] ARTIN [3] DWORK [5] GROTHENDIECK (Alexander). - Cohomologie l-adique et fonctions L , Séminaire de l’Institut des hautes Etudes scientifiques, Bures-sur-Yvette, 1964/65. ). - Cohomologie étale des schémas, Séminaire de l’Institut des hautes Etudes scientifiques, Bures-sur-Yvette, 1963/64. (Bernard). - On the rationality of the zeta function of an algebraic variety, Amer. J. , t. 82, 1960, p. 631-648. [4] GIRAUD (Jean). - Analysis situs, Séminaire Bourbaki, t. 15, 1962/63, n° 256, 11 p.

Algebraic fields and Hecke’s zeta functions groups. - 40 Princeton, Institute for ad- Séminaire BOURBAKI 17e année, 1964/65, n° 279 Décembre 1964 RATIONALITÉ FORMUIE DE LEFSCHETZ ET DES FONCTIONS L par Alexander GROTHENDIECK 1° Définitions des fonctions Z et L. fixe). schéma de type fini sur le corps premier F Mp On définit avec A. WEIL la fonction par où parcourt l’ensemble Soit le X degré nombre fini de Rappelons X des x(x) O[[t]] , corps résiduel du de séries formelles qu’un nombre premier Zy(t) x neau (p un points la formule est le nombre des x points fermés sur F .

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