Topic
Topological dynamics
About: Topological dynamics is a research topic. Over the lifetime, 1366 publications have been published within this topic receiving 41402 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: A novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets, and it is shown that these relations correspond to some of the standard set theoretical andTopological spatial Relations between sets such as equality, disjointness and containment in the interior.
Abstract: Practical needs in geographic information systems (GIS) have led to the investigation of formal and sound methods of describing spatial relations. After an introduction to the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering empty and non-empty as the values of the intersections, a total of sixteen topological spatial relations is described, each of which can be realized in R 2. This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space with an application to GIS. It is shown that these relations correspond to some of the standard set theoretical and topological spatial relations between sets such as equality, disjointness and containment in the interior.
1,699 citations
Book•
14 Jul 2014
TL;DR: The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press, to preserve the original texts of these important books while presenting them in durable paperback editions.
Abstract: Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
1,687 citations
Book•
1 Mar 2013
TL;DR: In this article, the authors present a Potpourri of stability results for Hyperbolic Sets and Markov Partitions for stable manifolds, as well as a list of notations.
Abstract: 1 Generalities.- 2 Filtrations.- 3 Sequences of Filtrations.- 4 Hyperbolic Sets.- 5 Stable Manifolds.- 6 Stable Manifolds for Hyperbolic Sets.- 7 More Consequences of Hyperbolicity.- 8 Stability.- 9 A Potpourri of Stability Results.- 10 Markov Partitions.- List of Notation.
980 citations
Book•
1 Feb 2003TL;DR: In this article, the Furstenberg-Zimmer structure theorem and host's theorem are derived from the Pinsker algebra, CPE and zero-entropy systems, and the relation between measure and topological entropy is discussed.
Abstract: Introduction General group actions: Topological dynamics Dynamical systems on Lebesgue spaces Ergodicity and mixing properties Invariant measures on topological systems Spectral theory Joinings Some applications of joinings Quasifactors Isometric and weakly mixing extensions The Furstenberg-Zimmer structure theorem Host's theorem Simple systems and their self-joinings Kazhdan's property and the geometry of $M_{\Gamma}(\mathbf{X})$ Entropy theory for $\mathbb{Z}$-systems: Entropy Symbolic representations Constructions The relation between measure and topological entropy The Pinsker algebra, CPE and zero entropy systems Entropy pairs Krieger's and Ornstein's theorems Prerequisite background and theorems Bibliography Index of symbols Index of terms.
909 citations
Book•
1 Mar 1992
TL;DR: In this paper, the authors studied the properties of periodic orbits and topological dynamics of the circle and showed that periodic orbits can be used to detect unstable manifolds and homoclinic points.
Abstract: Periodic orbits.- Turbulence.- Unstable manifolds and homoclinic points.- Topological dynamics.- Topological dynamics (continued).- Chaotic and non-chaotic maps.- Types of periodic orbits.- Topological Entropy.- Maps of the circle.
905 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 11 |
| 2024 | 11 |
| 2023 | 13 |
| 2022 | 38 |
| 2021 | 50 |