Integrating the nonintegrable: Analytic structure of the Lorentz system revisited
type: Item
instance of: scholarly article
title: Integrating the nonintegrable: Analytic structure of the Lorentz system revisited
zbMATH Open document ID: 0663.58042
DOI: 10.1016/S0167-2789(98)90018-5
author: S. H. Smith
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: A study of the complex time analytic structure of the Lorentz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one (time-dependent) integral of motion exists. Furthermore, the analysis yields the exact form of the integral with the highest homogeneous weight and a method to construct the rest of the integral. Recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument. The analytic techniques used in these studies, a systematic resummation of a logarithmic psi-series, appears to be quite general and can provide explicit representations of a solution - even in the chaotic regimes - in the neighborhood of a given movable singularity. Furthermore, we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4084629
zbMATH Keywords: Lorentz system in nonintegrable parameter regimes
zbMATH Keywords: Recursive clustering of singularities
zbMATH Keywords: singularity
zbMATH Keywords: nonintegrable systems
MaRDI profile type: Publication
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full work available at URL: s0167-2789(98)90018-5
OpenAlex ID: W1985659033
description: scientific article; zbMATH DE number 4084629