The Lefschetz zeta function associated to a continuous self-map f of a compact manifold is a rational function P/Q. According to the parity of the degrees of the polynomials P and Q, we analyze when the set of periodic points of f is infinite and when the topological entropy is positive.
@article{urn:eudml:doc:41728,
title = {Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {467-472},
mrnumber = {MR1209817},
zbl = {0777.58030},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41728}
}
Casasayas, Josefina; Llibre, Jaume, Nunes, Ana. Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.. Publicacions Matemàtiques, Tome 36 (1992) pp. 467-472. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41728/