Ergodic Theory and Dynamical Systems

Research Article

The Lyapunov dimension of a nowhere differentiable attracting torus

James L. Kaplana1, John Mallet-Pareta2 and James A. Yorkea3

a1 Department of Mathematics, Boston University, Boston, Massachusetts 02215, USA

a2 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

a3 Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA


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

(Received February 07 1983)

(Revised September 10 1983)