Infinite cascades of braids and smooth dynamical systems
type: Item
instance of: scholarly article
title: Infinite cascades of braids and smooth dynamical systems
zbMATH Open document ID: 0803.58046
DOI: 10.1016/0040-9383(94)90036-1
author: Jean-Marc Gambaudo
author: Charles Tresser
author: Dennis Sullivan
published in: Topology
publication date: 1994-03-24T00:00:00Z
review text: The authors consider the linking between orbits in a compact invariant set of a nonsingular vector field defined on a region in \(\mathbb{R}^ 3\). They discuss and compare some concepts of linking numbers of orbits and prove results concerning the behaviour of the sequence of the so-called average linking numbers between successive periodic orbits in the cascade generated by a \(C^ 1\)-flow on the solid torus and, then, reformulate this result in terms of an orientation preserving \(C^ 1\)-diffeomorphism of the 2-disk. They also show that, given a special sequence \((\ell_ n)\) of rational numbers, there exists a \(C^ 1\)-diffeomorphism (with zero topological entropy) of the 2-disk realizing a cascade of periodic orbits with the prescribed period and \(\ell_ n\) as the average linking number between successive orbits.
reviewed by: Wojciech Kryszewski
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 54C70
zbMATH DE Number: 527439
zbMATH Keywords: flow
zbMATH Keywords: periodic orbits
zbMATH Keywords: cascade
zbMATH Keywords: linking number
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)90036-1
OpenAlex ID: W2016706922
description: scientific article; zbMATH DE number 527439