Cremona transformation and general solution of one dynamical system of the static model
type: Item
instance of: scholarly article
title: Cremona transformation and general solution of one dynamical system of the static model
zbMATH Open document ID: 0759.39003
DOI: 10.1016/0167-2789(92)90007-A
author: K. V. Rerikh
published in: Physica D
publication date: 1993-01-16T00:00:00Z
review text: A particular quantum-physics problem is examined from an unusual point of view, because it is formulated in terms of an system of nonlinear difference equations. This system is considered to be equivalent to a second order quadratic Cremona map (QCM). Algebraic invariant curves of this QCM are determined explicitly. Short segments of two non-algebraic invariant curves crossing a saddle of the QCM are determined approximately by means of truncated series expansions. An asymptotic property of the latter is determined numerically. It is claimed that a general solution of the initial system has been constructed for one set of parameter values. An area preserving map is used in the argument without explaining how it is related qualitatively and quantitatively to an auxiliary dissipative map with a non-unity Jacobian.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 58D30
zbMATH DE Number: 94094
zbMATH Keywords: system of nonlinear difference equations
zbMATH Keywords: second order quadratic Cremona map
zbMATH Keywords: Algebraic invariant curves
zbMATH Keywords: truncated series expansions
zbMATH Keywords: asymptotic
reviewed by: Igor Gumowski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94094