Lattice Structures for Attractors II

The algebraic structure of the attractors in a dynamical system determines much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been mu...

Full description

Saved in:
Bibliographic Details
Published inFoundations of computational mathematics Vol. 16; no. 5; pp. 1151 - 1191
Main Authors Kalies, William D., Mischaikow, Konstantin, Vandervorst, Robert C. A. M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2016
Springer
Springer Nature B.V
Subjects
Algebra
Algebraic structures
Algorithms
Analysis
Applications of Mathematics
Attractors (mathematics)
Chaos theory
Collection
Computation
Computer Science
Dynamical systems
Dynamics
Economics
Foundations
Lattice theory
Lattices
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
United States
Distributive lattice
Secondary: 37B35
Primary: 37B25
Birkhoff’s representation theorem
Invariant set
Attracting neighborhood
Attractor
06D05
Online AccessGet full text

Cover

More Information
Summary:The algebraic structure of the attractors in a dynamical system determines much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics, which are capable of computing attracting neighborhoods efficiently. Here we address the question of whether all of the algebraic structure of attractors can be captured by these methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-015-9272-x