C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Sirvent, Víctor F. (Universidad Simón Bolívar. Departamento de Matemáticas (Venezuela))

Date:	2016
Abstract:	Let X be a connected closed manifold and f a self-map on X. We say that f is almost quasi-unipotent if every eigenvalue λ of the map f∗k (the induced map on the k-th homology group of X) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f∗k with k odd is equal to the sumof the multiplicities of λ as eigenvalue of all the maps f∗k with k even. We prove that if f is C1 having finitely many periodic points all of them hyperbolic, then f is almost quasi-unipotent.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Note:	Altres ajuts: ICREA Academia
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Hyperbolic periodic point ; Differentiable map ; Lefschetz number ; Lefschetz zeta function ; Quasi-unipotent map ; Almost quasi-unipotent map
Published in:	Mathematica Bohemica, Vol. 141, Issue 1 (2016) , p. 83-90, ISSN 2464-7136

DOI: 10.21136/MB.2016.6

8 p, 122.9 KB

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