An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane
type: Item
instance of: scholarly article
title: An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane
zbMATH Open document ID: 0622.58039
DOI: 10.1007/BF01239015
author: Gottfried Mayer-Kress
author: H. Haken
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: From a large class of diffeomorphisms in the plane, which are known to produce chaotic dynamics, we explicitly construct their continuous suspension on a three-dimensional cylinder. This suspension is smooth \((C^ 1)\) and can be characterized by the choice of two smooth functions on the unit interval, which have to fulfill certain boundary conditions. For the case of entire Cremona transformations, we are able to construct the corresponding autonomous differential equations of the flow explicitly. Thus it is possible to relate properties of discrete maps to those of ordinary differential equations in a quantitative manner. Furthermore, our construction makes it possible to study the exact solutions of chaotic differential-equations directly.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 4009397
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: Cremona transformations
zbMATH Keywords: chaotic differential-equations
MaRDI profile type: Publication
cites work: Q3908199
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description: scientific article; zbMATH DE number 4009397