Simple models for bifurcations creating horseshoes
type: Item
instance of: scholarly article
title: Simple models for bifurcations creating horseshoes
zbMATH Open document ID: 0587.58034
DOI: 10.1007/BF01008950
author: Jean-Marc Gambaudo
author: Charles Tresser
published in: Journal of Statistical Physics
publication date: 1983-01-01T00:00:00Z
review text: We present a class of simple models for global bifurcations creating horseshoes. Some properties known for Hénon mappings are easily obtained for these models such as, e.g., the existence of nontrivial hyperbolic sets. Kneading sequences techniques allow us to exhibit explicit differences with the global bifurcation diagram for maps of the interval. Explicit examples displaying wild hyperbolic sets and infinitely many sinks are also given as an illustration of the simplicity of these models.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 3942559
zbMATH Keywords: horseshoes
zbMATH Keywords: bifurcations
zbMATH Keywords: wild hyperbolic sets
zbMATH Keywords: infinitely many sinks
zbMATH Keywords: Hénon mappings
MaRDI profile type: Publication
cites work: Q4164074
cites work: Q3908199
cites work: On the Henon transformation
cites work: On computing the entropy of the Henon attractor
cites work: Shift automorphisms in the Henon mapping
cites work: Stable and unstable manifolds of the Henon mapping
cites work: A two-dimensional mapping with a strange attractor
cites work: Chaotic behavior in the Henon mapping
cites work: Q3814426
cites work: Existence of a homoclinic point for the Henon map
cites work: Diffeomorphisms with infinitely many sinks
cites work: On the nature of turbulence
cites work: Topological horseshoe and numerically observed chaotic behaviour in the Henon mapping
description: scientific article; zbMATH DE number 3942559