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Let be a connected closed manifold and a self-map on . We say that is almost quasi-unipotent if every eigenvalue of the map (the induced map on the -th homology group of ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of as eigenvalue of all the maps with odd is equal to the sum of the multiplicities of as eigenvalue of all the maps with even. We prove that if is having finitely many periodic points all of them hyperbolic,...
Soit un difféomorphisme lisse de fixant seulement l’origine, et son centralisateur dans le groupe des difféomorphismes . Des résultat classiques de Kopell et Szekeres montrent que est toujours un groupe à un paramètre. En revanche, Sergeraert a construit un dont le centralisateur est réduit au groupe des itérés de . On présente ici le résultat principal de [3] : peut en fait être un sous-groupe propre et non-dénombrable (donc dense) de .
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
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