C 1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Title:

C 1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Creator:

Llibre, Jaume and Sirvent, Víctor F.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0e6c3533-3951-4cea-86cd-d524d3e749ec
uuid:0e6c3533-3951-4cea-86cd-d524d3e749ec
doi:10.21136/MB.2016.6

Subject:

hyperbolic periodic point, differentiable map, Lefschetz number, Lefschetz zeta function, quasi-unipotent map, and almost quasi-unipotent map

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 sum of the multiplicities of λ as eigenvalue of all the maps f∗k with k even. We prove that if f is C 1 having finitely many periodic points all of them hyperbolic, then f is almost quasi-unipotent.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

83-90

Source:

Mathematica bohemica | 2016 Volume:141 | Number:1

Harvested from:

CDK

Metadata only:

false