Symbolic dynamics and nonlinear semiflows
type: Item
instance of: scholarly article
title: Symbolic dynamics and nonlinear semiflows
zbMATH Open document ID: 0632.58027
DOI: 10.1007/BF01760821
author: Jack K. Hale
author: Xiao-Biao Lin
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: The authors generalize results of Smale and of Shil'nikov about diffeomorphisms of manifolds to results about semiflows in Banach spaces. Smale showed that if q is a transverse homoclinic point then for some power of the map there is a ``horseshoe'' near the homoclinic point. This means that on this set the map is equivalent to a full 2 sided shift on two symbols. The authors generalize the necessary definitions and prove analogous results for semiflows on Banach spaces. They then discuss some of the consequences.
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 4028470
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: semiflows
zbMATH Keywords: transverse homoclinic point
MaRDI profile type: Publication
cites work: Homoclinic Points of Mappings of the Interval
cites work: Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978
cites work: Theory of functional differential equations. 2nd ed
cites work: Geometric theory of semilinear parabolic equations
cites work: Invariant manifolds
cites work: A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
cites work: On the Stable Manifold Theorem
cites work: ON THE SMOOTHNESS OF THE COMPOSITION MAP
cites work: Period Three Implies Chaos
cites work: Snap-back repellers imply chaos in \(\mathbb{R}^n\)
cites work: Stable and Random Motions in Dynamical Systems
cites work: Q3952851
cites work: Exponential dichotomies and transversal homoclinic points
cites work: ON A POINCARÉ-BIRKHOFF PROBLEM
cites work: Q5518129
cites work: Differentiable dynamical systems
cites work: Homoclinic solution and chaos in
full work available at URL: https://doi.org/10.1007/bf01760821
OpenAlex ID: W1999585119
description: scientific article; zbMATH DE number 4028470