Finite Resolution Dynamics

• Published in: Foundations of computational mathematics Vol. 11; no. 2; pp. 211 - 239
• Main Authors: Luzzatto, Stefano, Pilarczyk, Paweł
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.04.2011; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Approximation; Combinatorial analysis; Combinatorics; Computer Science; Dynamical systems; Economics; Equivalence; Finite element analysis; Foundations; Graphs; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Matrix Theory; Numerical Analysis; Open cover; 37M99; Mixing; Rigorous numerics; 65G20; Dynamical system; Combinatorial dynamics; Transitivity; Algorithm; 65P20; Finite resolution; Directed graph

We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given number. Open covers are used to approximate the topology of the...