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The Lyapunov dimension of a nowhere differentiable attracting torus

Published online by Cambridge University Press:  19 September 2008

James L. Kaplan ,
John Mallet-Paret  and
James A. Yorke
James L. Kaplan
Affiliation:
Department of Mathematics, Boston University, Boston, Massachusetts 02215, USA
John Mallet-Paret
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 and Lefschetz Centre for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
James A. Yorke
Affiliation:
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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Abstract

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The fractal dimension of an attracting torus Tk in × Tk is shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. The cases studied here can have several Lyapunov numbers greater than 1 and several less than 1

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 261 - 281
Copyright
Copyright © Cambridge University Press 1984

References

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