Results and open questions on some invariants measuring the dynamical complexity of a map

Jaume Llibre, and Radu Saghin. "Results and open questions on some invariants measuring the dynamical complexity of a map." Fundamenta Mathematicae 206.1 (2009): 307-327. <http://eudml.org/doc/283084>.

@article{JaumeLlibre2009,
abstract = {Let f be a continuous map on a compact connected Riemannian manifold M. There are several ways to measure the dynamical complexity of f and we discuss some of them. This survey contains some results and open questions about relationships between the topological entropy of f, the volume growth of f, the rate of growth of periodic points of f, some invariants related to exterior powers of the derivative of f, and several invariants measuring the topological complexity of f: the degree (for the case when the manifold is orientable), the spectral radius of the map induced by f on the homology of M, the fundamental-group entropy, the asymptotic Lefschetz number and the asymptotic Nielsen number. In general these relations depend on the smoothness of f. Various examples are provided.},
author = {Jaume Llibre, Radu Saghin},
journal = {Fundamenta Mathematicae},
keywords = {spectral radius; degree; asymptotic Lefschetz number; fundamental-group entropy; asymptotic Nielsen number; topological entropy; volume growth; rate of growth of periodic points},
language = {eng},
number = {1},
pages = {307-327},
title = {Results and open questions on some invariants measuring the dynamical complexity of a map},
url = {http://eudml.org/doc/283084},
volume = {206},
year = {2009},
}

TY - JOUR
AU - Jaume Llibre
AU - Radu Saghin
TI - Results and open questions on some invariants measuring the dynamical complexity of a map
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 307
EP - 327
AB - Let f be a continuous map on a compact connected Riemannian manifold M. There are several ways to measure the dynamical complexity of f and we discuss some of them. This survey contains some results and open questions about relationships between the topological entropy of f, the volume growth of f, the rate of growth of periodic points of f, some invariants related to exterior powers of the derivative of f, and several invariants measuring the topological complexity of f: the degree (for the case when the manifold is orientable), the spectral radius of the map induced by f on the homology of M, the fundamental-group entropy, the asymptotic Lefschetz number and the asymptotic Nielsen number. In general these relations depend on the smoothness of f. Various examples are provided.
LA - eng
KW - spectral radius; degree; asymptotic Lefschetz number; fundamental-group entropy; asymptotic Nielsen number; topological entropy; volume growth; rate of growth of periodic points
UR - http://eudml.org/doc/283084
ER -