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

• Autorzy: Jaume Llibre , Radu Saghin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37B40: Topological entropy
• 37C05: Smooth mappings and diffeomorphisms
• 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
• 37-02: Research exposition (monographs, survey articles)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 307-327

Daty

wydano

2009

Twórcy

autor

Jaume Llibre

• Departament de Matematiques, Universitat Autonoma de Barcelona, Bellaterra, 08193, Spain

autor

Radu Saghin

• Centre de Recerca Matematica, Apartat 50, Bellaterra, 08193, Spain

Identyfikatory

DOI

10.4064/fm206-0-19