topological dynamics

topological dynamics

[¦täp·ə¦läj·ə·kəl dī′nam·iks]
(mathematics)
The study and application of transformations, or groups of such transformations (particularly topological transformation groups), defined on a topological space (usually compact), with particular regard to properties of interest in the qualitative theory of differential equations.
References in periodicals archive ?
Balibrea, "On problems of topological dynamics in non-autonomous discrete systems," Applied Mathematics and Nonlinear Sciences, vol.
Their topics include the enumeration of degrees: local and global structural interactions, Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: some results and an open problem, open problems on ultrafiltration and some connections to the continuum, obtaining Woodin's cardinals, translation procedures in descriptive inner model theory, and set-theoretic foundations.
Objective: The aim of the project is to investigate the phenomenon of universality in Topological Dynamics. Universality is a classical and fundamental subject in Dimension Theory.
Rather than add yet another to the many good general descriptions of dynamical systems, Bollt and Santitissadeekorn draw connections between topological dynamics, symbolic dynamics, and information theory to show that these are also highly relevant to the Ulam-Galerkin representations.
In consideration of the above-mentioned motives, based on a time-varying copula approach and the MST method, we aim to construct time-varying FX networks and analyze their topological dynamics and market properties.
Todorcevic, Fraisse limits, Ramsey theory, and topological dynamics ofautomorphism groups, Geom.
With material from the first year of the blog already published in book form, this book is the first volume of a two-volume set of blog posts from 2008, focusing on ergodic theory, topological dynamics, combinatorics, and number theory.
They cover topological data analysis, topological dynamics: rigorous numerics via cubical homology, Euler calculus with applications to signals and sensing, the topology of discrete planning with uncertainty, and the combinatorial optimization of cycles and bases.
Initial chapters are devoted to fundamental topology and measure theory, and symbolic and topological dynamics. Two chapters use combinatoric, number theoretic, and symbolic machinery in a discussion of one-dimensional dynamical systems.
Then they explore some applications of the algebra to the part of combinatorics known as Ramsey Theory and demonstrate its connections with topological dynamics, ergodic theory, and the general theory of semigroup compactifications.
Conference on Algebraic and Topological Dynamics (2004: Bonn, Germany) Ed.