On the global structure of period doubling flows
type: Item
instance of: scholarly article
title: On the global structure of period doubling flows
zbMATH Open document ID: 0594.58038
DOI: 10.1016/0167-2789(84)90275-6
author: John David Crawford
author: Stephen Omohundro
published in: Physica D
publication date: 1984-01-01T00:00:00Z
full work available at URL: 2dt497v3
review text: For a wide class of period doubling flows on \(R^ 3\) the global structure of the invariant manifolds and the topology of the bifurcating periodic orbits are analyzed. The global manifold structure implies constraints for the subsequent bifurcational behavior of the flows. The period doubled orbits are classified using the theory of iterated torus knots. This classification reveals an infinite number of topologically distinct period doubling flows and raises the important question as to which sequences of torus knots appear in the asymptotic limit of a period doubling cascade. If the asymptotic sequence of torus knots produced is not unique, then the self-similarity of the Poincaré map does not imply a self-similar structure for the flows. In particular, at the accumulation point for the cascade, one would not expect to observe a universal power spectrum for the flow. This possibility is of some experimental interest.
reviewed by: Sattor Baĭzaev
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 3956053
zbMATH Keywords: flows
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: vector fields
zbMATH Keywords: invariant manifolds
zbMATH Keywords: orbits
zbMATH Keywords: period doubling flows
zbMATH Keywords: bifurcating periodic orbits
MaRDI profile type: Publication
OpenAlex ID: W2069334083
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description: scientific article; zbMATH DE number 3956053