Computer assisted proof of chaos in the Lorenz equations

Zbigniew Galias, Piotr Zgliczyński

Type: Article

Publication Date: 1998-05-01

Citations: 84

DOI: https://doi.org/10.1016/s0167-2789(97)00233-9

View Publication

Locations

Physica D Nonlinear Phenomena - View

Similar Works

Action	Title	Year	Authors
+	Chaos in the Lorenz Equations: A Computer Assisted Proof Part III: Classical Parameter Values	2001	Konstantin Mischaikow Marian Mrożek Andrzej Szymczak
+	A computer proof that the Lorenz equations have “chaotic” solutions	1994	Brian Hassard J. Zhang S. P. Hastings William C. Troy
+	Analytical prediction of the transition to chaos in Lorenz equations	2010	Péter Vadász
+	Chaos control for the Lorenz system	2018	Pedro Pablo Cárdenas Álzate Germán Correa Vélez Fernando Mesa
+	Computer program for Lorenz equations	1997
+	Computer program for Lorenz equations	2004
+	Chaos in the Kuramoto–Sivashinsky equations—a computer-assisted proof	2003	Daniel Wilczak
+ PDF Chat	Analytical study of chaos and applications	2016	G. Contopoulos M. Harsoula Christos Efthymiopoulos
+ PDF Chat	Chaos in a generalized Lorenz system	2008	E. D. Belokolos Vasyl O. Kharchenko Dmitrii O. Kharchenko
+	Visualizing the transition to chaos in the Lorenz system	2006	Hinke M. Osinga Bernd Krauskopf EJ Doedel
+	A computer-assisted proof for the existence of horseshoe in a novel chaotic system	2008	Wenjuan Wu Zengqiang Chen Zhuzhi Yuan
+	A Review and Demonstration of The Essence of Chaos by Edward N. Lorenz	2009	Robert H. Lurie
+ PDF Chat	Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system	2018	Maciej J. Capiński Dmitry Turaev Piotr Zgliczyński
+	Rigorous proof of chaos in the double-scroll system	2010
+	Information enciphering based on chaotic solutions of deterministic equations	2005	G. N. Kal’yanov Ér. V. Kal’yanov
+	Rigorous models for the Lorenz equations	1996	Warwick Tucker
+	Analysis for chaos and fractals in nonlinear dynamical systems	1990	Sanjeev Khanna
+	The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos	2010	Charlotte Werndl
+	Structure-Preserving Algorithms for the Lorenz System	2008	江铁强梅凤翔陈立杰
+	Solution bounds of generalized Lorenz chaotic systems	2007	Yeong‐Jeu Sun

Works That Cite This (59)

Action	Title	Year	Authors
+ PDF Chat	A Lorenz-type attractor in a piecewise-smooth system: Rigorous results	2019	В. Н. Белых Nikita V. Barabash Igor Belykh
+ PDF Chat	Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs	2021	В. Н. Белых Nikita V. Barabash Igor Belykh
+ PDF Chat	Rigorous study of short periodic orbits for the Lorenz system	2008	Zbigniew Galias Warwick Tucker
+	Rigorous numerics for a singular perturbation problem	2019	Aleksander Czechowski
+ PDF Chat	Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds	2018	William D. Kalies Shane Kepley J. D. Mireles James
+	Covering relations, cone conditions and the stable manifold theorem	2009	Piotr Zgliczyński
+	Isolating Segments, Fixed Point Index, and Symbolic Dynamics	2000	Klaudiusz Wójcik Piotr Zgliczyński
+	Symbolic Dynamics for the Hénon–Heiles Hamiltonian on the Critical Level	2001	Gianni Arioli Piotr Zgliczyński
+ PDF Chat	A Rigorous ODE Solver and Smale’s 14th Problem	2002	Warwick Tucker
+	Covering relations for multidimensional dynamical systems	2004	Piotr Zgliczyński Marian Gidea

Works Cited by This (23)

Action	Title	Year	Authors
+	Lectures on algebraic topology	1967	Marvin J. Greenberg
+	Isolated Invariant Sets and the Morse Index	1978	Charles C. Conley
+	Positive Topological Entropy of Chua's Circuit: A Computer Assisted Proof	1997	Zbigniew Galias
+	On the Strange Attractor and Transverse Homoclinic Orbits for the Lorenz Equations	1995	H. Spreuer E. Eric Adams
+	Isolating blocks and epsilon chains for maps	1989	Robert W. Easton
+	CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS	1994	L. P. Shilnikov
+ PDF Chat	The structure of Lorenz attractors	1979	R. F. Williams
+	Isolating neighborhoods and chaos	1995	Konstantin Mischaikow Marian Mrożek
+ PDF Chat	Solving ordinary differential equations I. nonstiff problems	1987	Ernst Hairer Syvert P. Nørsett Gerhard Wanner
+	Isolating blocks and symbolic dynamics	1975	Robert W. Easton