Scientific publications on the Lorenz manifold

Animation of the Lorenz manifold rotating about the z-axis
We have published several papers on the Lorenz manifold in scientific journals. Quite a lot of these include animations or come with dedicated multimedia supplements. While these papers do assume a basic calculus background, we believe that they are suitable for a non-specialist audience with an interest in dynamical systems.

Crocheting the Lorenz manifold

Crocheting the Lorenz manifold
Hinke M. Osinga & Bernd Krauskopf
The Mathematical Intelligencer 26(4): 25-37, 2004
This paper cannot be downloaded, but the preprint containing the crochet instructions is available

The Lorenz equations and the Lorenz manifold

The Lorenz manifold as a collection of geodesic level sets
Bernd Krauskopf & Hinke M. Osinga
Nonlinearity 17(1): C1-C6, 2004
This paper can be downloaded for free and comes with a dedicated multimedia supplement
  
Visualizing the structure of chaos in the Lorenz system
Hinke M. Osinga & Bernd Krauskopf
Computers & Graphics 26(5): 815-823, 2002
This paper is accessible subject to subscription, but the preprint can be downloaded for free.

The algorithm and computations of the Lorenz manifold

A survey of methods for computing (un)stable manifolds of vector fields
Bernd Krauskopf, Hinke M. Osinga, Eusebius J. Doedel, Michael E. Henderson, John M. Guckenheimer, Alexander Vladimirsky, Michael Dellnitz & Oliver Junge
Int. J. Bifurcation & Chaos 15(3): 763-791, 2005
This paper is accessible subject to subscription, but the preprint can be downloaded for free.
  
Computing geodesic level sets on global (un)stable manifolds of vector fields
Bernd Krauskopf & Hinke M. Osinga
SIAM Journal on Applied Dynamical Systems 2(4): 546-569, 2003
This paper can be downloaded for free and has associated animations. The two showing the Lorenz manifold are linked from the images on the right.
  
Two-dimensional global manifolds of vector fields
Bernd Krauskopf & Hinke M. Osinga
Chaos 9(3): 768-774, 1999
This paper comes with a dedicated multimedia supplement; the text is accessible subject to subscription, but the preprint can be downloaded for free.
  
Globalizing two-dimensional unstable manifolds of maps
Bernd Krauskopf & Hinke M. Osinga
Int. J. Bifurcation & Chaos 8(3): 483-503, 1998
This paper contains our first image of the Lorenz manifold; it is accessible subject to subscription, but a multimedia electronic preprint can be viewed for free.


Copyright © 2005 by Hinke Osinga & Bernd Krauskopf
Last modified: Fri Apr 11 16:57:52 NZST 2014