Invariant geometric properties of class of 3D chaotic flows
type: Item
instance of: scholarly article
title: Invariant geometric properties of class of 3D chaotic flows
zbMATH Open document ID: 0959.37015
DOI: 10.1016/S0167-2789(99)00240-7
author: Massimiliano Giona
author: Alessandra Adrover
published in: Physica D
publication date: 2001-04-24T00:00:00Z
review text: The paper deals with \(C^{\infty}\) volume-preserving diffeomorphisms \(\Phi = \mathcal H^{-1} \circ \mathcal A \circ \mathcal H\) of the \(3\)-dimensional torus \(T^3\) topologically conjugate to a linear map \(\mathcal A(x)\) where \(\circ\) indicates composition and \(\mathcal H(x)\) is a generic \(C^{\infty}\) volume-preserving diffeomorphism. The authors determine the global geometrical properties and the resulting pointwise characterization of the evolution of curves and surfaces advected by the diffeomorphism \(\Phi.\) The measure-theoretical properties associated with the asymptotic evolution of so-called material lines and surfaces are analyzed. The connection between the theory of the asymptotic properties of the diffeomorphism \(\Phi\) and the properties of physically realizable \(3\)-dimensional chaotic flows is discussed.
Mathematics Subject Classification ID: 37C05
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 1496380
zbMATH Keywords: 3D torus
zbMATH Keywords: diffeomorphism
zbMATH Keywords: asymptotic
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
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Wikidata QID: Q128141949
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description: scientific article; zbMATH DE number 1496380