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

Llibre, Jaume, and Sirvent, Víctor F.. "$C^1$ self-maps on closed manifolds with finitely many periodic points all of them hyperbolic." Mathematica Bohemica 141.1 (2016): 83-90. <http://eudml.org/doc/276767>.

@article{Llibre2016,
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 $\lambda $ 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 $\lambda $ as eigenvalue of all the maps $f_\{*k\}$ with $k$ odd is equal to the sum of the multiplicities of $\lambda $ 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.},
author = {Llibre, Jaume, Sirvent, Víctor F.},
journal = {Mathematica Bohemica},
keywords = {hyperbolic periodic point; differentiable map; Lefschetz number; Lefschetz zeta function; quasi-unipotent map; almost quasi-unipotent map},
language = {eng},
number = {1},
pages = {83-90},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$C^1$ self-maps on closed manifolds with finitely many periodic points all of them hyperbolic},
url = {http://eudml.org/doc/276767},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Llibre, Jaume
AU - Sirvent, Víctor F.
TI - $C^1$ self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 1
SP - 83
EP - 90
AB - 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 $\lambda $ 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 $\lambda $ as eigenvalue of all the maps $f_{*k}$ with $k$ odd is equal to the sum of the multiplicities of $\lambda $ 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.
LA - eng
KW - hyperbolic periodic point; differentiable map; Lefschetz number; Lefschetz zeta function; quasi-unipotent map; almost quasi-unipotent map
UR - http://eudml.org/doc/276767
ER -