Factorisation of Lefschetz zeta functions and twisted periodic orbits
type: Item
instance of: scholarly article
title: Factorisation of Lefschetz zeta functions and twisted periodic orbits
zbMATH Open document ID: 0818.58038
DOI: 10.1007/BF02571937
author: Mark Pollicott
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174683
review text: Let \(x\) be a periodic point of period \(n\) for a diffeomorphism \(f\) of a compact manifold. Denote by \(E^ u_ x\) the frame spanned by the eigenvectors of \(Df^ n(x)\) that correspond to the eigenvalues \(\lambda\) with \(| \lambda | > 1\). The point \(x\) is called twisted if \(Df^ n(x)\) reverses the orientation of \(E^ u_ x\). The author constructs a new factorization of the Lefschetz zeta function for \(f\) and studies its connection with the existence of twisted periodic orbits (t.p.o. below). For example, for a surface diffeomorphism conditions are given under which the existence of one t.p.o. implies the existence of a countable family of t.p.o.
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 704941
zbMATH Keywords: factorization
zbMATH Keywords: Lefschetz zeta function
zbMATH Keywords: twisted periodic orbits
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
cites work: Period Doubling and the Lefschetz Formula
cites work: Some Smooth Maps with Infinitely Many Hyperbolic Peridoic Points
cites work: Q3999409
cites work: Differentiable dynamical systems
cites work: On the geometry and dynamics of diffeomorphisms of surfaces
OpenAlex ID: W2068063144
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description: scientific article; zbMATH DE number 704941