Skip to main content
SpringerLink
Log in

Lorenz Cross-Sections and Dimension of the Double Rotor Attractor

  • Conference paper
Dimensions and Entropies in Chaotic Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 32))

  • 552 Accesses

Abstract

A Lorenz cross-section of an attractor in Rn with k > 0 positive Lyapunov exponents is the transverse intersection of the attractor with an n − k dimensional plane. We outline a numerical procedure to compute Lorenz cross-sections of chaotic attractors with k > 1 positive Lyapunov exponents and apply the technique to the attractor produced by the double rotor map, two of whose numerically computed Lyapunov exponents are positive and whose Lyapunov dimension is 3.64. The pointwise dimension of the Lorenz cross-sections is computed approximately as 1.64. This numerical evidence supports a conjecture that the pointwise and Lyapunov dimensions of typical attractors are equal.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. N. Lorenz, Physica 13D, 90 (1984).

    MathSciNet  ADS  Google Scholar 

  2. J. D. Farmer, E. Ott and J. A. Yorke, Physica 7D, 153 (1983).

    MathSciNet  ADS  Google Scholar 

  3. J. P. Eckmann and D. Ruelle, Rev. Mod. Phys. 54, 153 (1983).

    Google Scholar 

  4. J. L. Kaplan and J. A. Yorke, in Functional Differential Equations and Approximation of Fixed Points, H. O. Peitgen and H O. Walther (eds.), pp. 228–237. Springer Lecture Notes in Mathematics, Vol. 730. (New York: Springer-Verlag, 1979).

    Google Scholar 

  5. E. Kostelich, C. Grebogi, E. Ott and J. A. Yorke, in preparation.

    Google Scholar 

  6. E. Kostelich and J. A. Yorke, in preparation.

    Google Scholar 

Download references

Author information

Author notes

  1. E. J. Kostelich

    Present address: Department of Physics and Center for Nonlinear Dynamics, University of Texas, Austin, Texas, 78712, USA

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    E. J. Kostelich

  2. Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA

    J. A. Yorke

Authors
  1. E. J. Kostelich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Yorke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Nonlinear Studies, Los Alamos National Laboratory, Mail Stop: B258, Los Alamos, NM, 87545, USA

    Gottfried Mayer-Kress

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kostelich, E.J., Yorke, J.A. (1986). Lorenz Cross-Sections and Dimension of the Double Rotor Attractor. In: Mayer-Kress, G. (eds) Dimensions and Entropies in Chaotic Systems. Springer Series in Synergetics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71001-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-71001-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71003-2

  • Online ISBN: 978-3-642-71001-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation