Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T01:02:02.023Z Has data issue: false hasContentIssue false
  • English
  • Français

The topological classification of Lorenz attractors

Published online by Cambridge University Press:  24 October 2008

David Rand
David Rand
Affiliation:
University of Warwick
Get access Rights & Permissions [Opens in a new window]

Extract

The Lorenz attractor is a strange attractor which has been proposed as an explicit model for turbulence ((4), compare (5)). First studied by E. N. Lorenz as a truncation of the Navier-Stokes equations (2), it has since attracted the attention of mathematicians because of its particularly interesting dynamical properties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 3 , May 1978 , pp. 451 - 460
Copyright
Copyright © Cambridge Philosophical Society 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Guckenheimer, J. A strange, strange attractor, in J. Marsden and M. McCracken. The Hopf bifurcation (Springer Lecture Notes in Applied Mathematics, 1976).CrossRefGoogle Scholar
(2)Lorenz, E. N.Deterministic nonperiodic flow. J. of Atmospheric Sciences 20 (1963), 130–141.2.0.CO;2>CrossRefGoogle Scholar
(3)Milnor, J. ‘The theory of kneading’ and ‘A piecewise linear model for kneading’, Unpublished notes, 1976.Google Scholar
(4)Ruelle, D. The Lorenz attractor and the problem of turbulence, to appear in The Proceed-ings of the Conference on Quantum Models and Mathematics, Bielefeld, 1975.CrossRefGoogle Scholar
(5)Ruelle, D. and Takens, F.On the nature of turbulence. Comm. Math. Physics 20 (1971), 167–192;CrossRefGoogle Scholar
Ruelle, D. and Takens, F.On the nature of turbulence. Comm. Math. Physics 23 (1971), 343–344.CrossRefGoogle Scholar
(6)Williams, R. F.The structure of Lorenz attractors (preprint, 1976).CrossRefGoogle Scholar
(7)Jonker, L.Periodic orbits and kneading invariants (Warwick University Preprint, 1977).Google Scholar