Lorenz attractor through saddle-node bifurcations
type: Item
instance of: scholarly article
title: Lorenz attractor through saddle-node bifurcations
zbMATH Open document ID: 0871.58061
DOI: 10.1016/S0294-1449(16)30116-0
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1997-06-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78394
review text: A geometric Lorenz attractor is a vector field in \(\mathbb{R}^3\) which has an attractor with a dense set of hyperbolic period orbits and one hyperbolic singularity. A saddle-node Lorenz attractor is, as defined in the paper, a three-dimensional vector field for which its nonwandering set consists of a hyperbolic set together with an attractor in which there exists a dense set of periodic hyperbolic orbits and at least one saddle-node singularity. The paper realises a study of the unfolding of such attractors through a saddle-node bifurcation.
reviewed by: Iuliana Oprea
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 936275
zbMATH Keywords: Lorenz attractor
zbMATH Keywords: saddle-node bifurcation
zbMATH Keywords: homoclinic tangency
author: C. A. Morales
MaRDI profile type: Publication
cites work: ON ATTAINABLE TRANSITIONS FROM MORSE-SMALE SYSTEMS TO SYSTEMS WITH MANY PERIODIC MOTIONS
cites work: The explosion of singular cycles
cites work: Strange attractors in saddle-node cycles: Prevalence and globality
cites work: Structural stability of Lorenz attractors
cites work: Q5618790
cites work: Invariant manifolds
cites work: Q3138991
cites work: Deterministic Nonperiodic Flow
cites work: Abundance of strange attractors
cites work: Q3888200
cites work: Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
cites work: SOURCES AND SINKS OFA-DIFFEOMORPHISMS OF SURFACES
cites work: Stability of parametrized families of gradient vector fields
cites work: Q4003408
cites work: Differentiable dynamical systems
cites work: Q4049841
cites work: Partially hyperbolic fixed points
cites work: One-dimensional non-wandering sets
description: scientific article; zbMATH DE number 936275