On the symmetry lines of the standard mapping
type: Item
instance of: scholarly article
title: On the symmetry lines of the standard mapping
zbMATH Open document ID: 0612.58023
DOI: 10.1016/0167-2789(87)90236-3
author: E. Piña
author: Lidia Jiménez-Lara
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: The Taylor and Chirikov standard mapping is used as a model to represent the dynamics of non-integrable systems by means of the Poincaré section of the trajectories intersecting a fixed plane of the phase space. This study is based on a systematic use of the decomposition of the standard mapping in a product of two involutions, forming a group including the iterates of the mapping and their inverses. The symmetry lines of the family of involutions determine the position of the periodic points and explain the onset of new chains of periodic points produced by the winding of the symmetry lines around the stable periodic points.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 3990443
zbMATH Keywords: Taylor and Chirikov standard mapping
zbMATH Keywords: dynamics of non-integrable systems
zbMATH Keywords: Poincaré section
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90236-3
OpenAlex ID: W2036503556
cites work: Q5838030
cites work: Q3244060
cites work: Q3953228
cites work: Q4167627
cites work: Q3260726
cites work: Q3953310
cites work: Two-Dimensional Measure-Preserving Mappings
cites work: A mathematical critique of some physical theories
cites work: A renormalization approach to invariant circles in area-preserving maps
cites work: Universal behaviour in families of area-preserving maps
cites work: On the stability of periodic orbits of two-dimensional mappings
cites work: Critical Behavior of a KAM surface. I: Empirical results
cites work: The Lattice Point Covering Theorem for Rectangles
cites work: On universality for area-preserving maps of the plane
cites work: Q5555054
description: scientific article; zbMATH DE number 3990443