Knotted periodic orbits in dynamical systems—I: Lorenz's equation

Joan S. Birman, R. F. Williams

Type: Article

Publication Date: 1983-01-01

Citations: 293

DOI: https://doi.org/10.1016/0040-9383(83)90045-9

View Publication

Locations

Topology - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Branched manifolds for the three types of unimodal maps	2021	Christophe Letellier
+	On the topology of the Lü attractor and related systems	2008	Stavros Anastassiou Tassos Bountis Y. G. Petalas
+	BEHAVIOR PATTERNS IN MULTIPARAMETRIC DYNAMICAL SYSTEMS: LORENZ MODEL	2012	Roberto Barrio Fernando Blesa Sergio Serrano
+ PDF Chat	Topological characterization of toroidal chaos: A branched manifold for the Deng toroidal attractor	2021	Sylvain Mangiarotti Christophe Letellier
+	Topological classification of periodic orbits in Lorenz system	2018	Chengwei Dong
+	Required criteria for recognizing new types of chaos: Application to the “cord” attractor	2012	Christophe Letellier Luís A. Aguirre
+	Bifurcations of Chaotic Attractors in a Piecewise Smooth Lorenz-Type System	2020	В. Н. Белых Nikita V. Barabash Igor Belykh
+ PDF Chat	The Lorenz Attractor, a Paradigm for Chaos	2013	Étienne Ghys
+	Lorenz Attractors and Generalizations: Geometric and Topological Aspects	2014	Наталья Эдуардовна Клиншпонт
+	Topological study of the Lorenz convection model's random attractor (LORA)	2019	Denisse Sciamarella Michael Ghil Gisela Daniela Charó
+ PDF Chat	A Lorenz-type attractor in a piecewise-smooth system: Rigorous results	2019	В. Н. Белых Nikita V. Barabash Igor Belykh
+ PDF Chat	On the topology of the Lorenz system	2017	Tali Pinsky
+	Knots and Chaos in the Rössler System	2023	Eran Igra
+	Entropy charts and bifurcations for Lorenz maps with infinite derivatives	2021	Mikhail Malkin Klim Safonov
+	Topological classification of periodic orbits in the generalized Lorenz-type system with diverse symbolic dynamics	2021	Chengwei Dong Huihui Liu Qi Jie Hantao Li
+	Periodic orbit analysis of the Lorenz attractor	1994	Bruno Eckhardt Gerolf Ott
+	Topology of Lorenz-like attractors	2019
+ PDF Chat	Geometrical and dynamical properties of Lorenz type system	2005	Natal'ya Eduardovna Klinshpont Евгений Анатольевич Сатаев Romen V Plykin
+ PDF Chat	Resonances in a Chaotic Attractor Crisis of the Lorenz Flow	2017	Alexis Tantet Valerio Lucarini Henk A. Dijkstra
+	On the topological classification of Lorenz-type attractors	2006	Наталья Эдуардовна Клиншпонт

Works That Cite This (228)

Action	Title	Year	Authors
+	Computation of symbolic dynamics for one-dimensional maps	2010	Lorenzo Sella Pieter Collins
+	Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization	2023	Tali Pinsky
+ PDF Chat	Chaos in variable stars: Topological analysis of W Vir model pulsations	1996	Christophe Letellier G. Gouesbet F. Soufi J. R. Buchler Z. Kolláth
+	Topological colouring of fluid particles unravels finite-time coherent sets	2021	Gisela D. Charó Guillermo Artana Denisse Sciamarella
+	UNIVERSAL FORM OF RENORMALIZABLE KNOTS IN SYMBOLIC DYNAMICS OF BIMODAL MAPS	2013	Wen Gao Chuanyun Xu Shou-Li Peng Ke‐Fei Cao
+	Unveiling the topological structure of chaotic flows from data	2001	Denisse Sciamarella Gabriel B. Mindlin
+	Algebraic evaluation of linking numbers of unstable periodic orbits in chaotic attractors	1994	L. Le Sceller Christophe Letellier G. Gouesbet
+	Confinor and Anti-confinor in Constrained “Lorenz” System	1987	Shigehiro Ushiki René Lozi
+	Knots motivated by discrete dynamical systems	2001	E. Ahmed E. A. Elrifai
+	Computer evaluation of Homfly polynomials by using Gauss codes, with a skein-template algorithm	1999	G. Gouesbet S. Meunier-Guttin-Cluzel Christophe Letellier

Works Cited by This (27)

Action	Title	Year	Authors
+	Lecture VII The structure of lorenz attractors	1977	R. F. Williams
+	Singular points of complex hypersurfaces	1968	John Milnor
+	Braids, Links, and Mapping Class Groups	1974	Joan S. Birman
+	On fibering certain 3-manifolds	1961	John R. Stallings
+	Knots and Links	1976	Dale Rolfsen
+	A Strange, Strange Attractor	1976	John Guckenheimer
+	Hyperbolicity and chain recurrence	1977	John E. Franke James F. Selgrade
+ PDF Chat	The structure of Lorenz attractors	1979	R. F. Williams
+	Non-singular Morse–Smale flows on 3-dimensional manifolds	1979	John W. Morgan
+ PDF Chat	Stable manifolds for hyperbolic sets	1969	Morris W. Hirsch Charles Pugh