The Lorenz manifold as a collection of geodesic level sets

Nonlinearity

Volumn 17, Issue 1, 2004, Pages

  Krauskopf, Bernd ^a   Osinga, Hinke M ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347931873     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/1/000     Document Type: Review

References (14)

1. Abraham R H and Shaw C D 1985 Dynamics - The Geometry of Behavior, Part Three: Global Behavior (Santa Cruz, CA: Aerial Press)
2. Dellnitz M and Hohmann A 1997 A subdivision algorithm for the computation of unstable manifolds and global attractors Numer. Math. 75 293-317
3. Doedel E J 1997 private communications at the IMA, Minneapolis
4. Guckenheimer J and Holmes P 1986 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields 2nd edn (Berlin: Springer)
5. Guckenheimer J and Vladimirsky A 2003 A fast method for approximating invariant manifolds Preprint http://www.math.cornell.edu/̃vlad/papers/InvMfolds/InvMfolds.pdf
6. Guckenheimer J and Worfolk P 1993 Dynamical systems: some computational problems Bifurcations and Periodic Orbits of Vector Fields ed D Schlomiuk (Dordrecht: Kluwer) pp 241-77
7. Henderson M E 2003 Computing invariant manifolds by integrating fattened trajectories Preprint
8. Johnson M E, Jolly M S and Kevrekidis I G 1997 Two-dimensional invariant manifolds and global bifurcations: some approximation and visualization studies Numer. Algorithms 14 125-40
9. Krauskopf B and Osinga H M 1999 Two-dimensional global manifolds of vector fields Chaos 9 768-74
10. Krauskopf B and Osinga H M 2002 Visualizing the structure of chaos in the Lorenz system Comput. Graph. 26 815-23
11. Krauskopf B and Osinga H M 2003 Computing geodesic level sets on global (un)stable manifolds of vector fields SIAM J. Appl. Dyn. Syst. at press
12. Lorenz E N 1963 Deterministic nonperiodic flows J. Atmos. Sci. 20 130-41
13. Phillips M, Levy S and Munzner T 1993 Geomview: an interactive geometry viewer Notices Am. Math. Soc. 40 985-8
14. Strogatz S H 1994 Nonlinear Dynamics and Chaos (Reading, MA: Addison-Wesley)