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  • Ergodic Theory and Dynamical Systems, Volume 4, Issue 2
  • June 1984, pp. 261-281

The Lyapunov dimension of a nowhere differentiable attracting torus

  • James L. Kaplan (a1), John Mallet-Paret (a2) and James A. Yorke (a3)
  • DOI:
  • Published online: 01 September 2008

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

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[8]G. H. Hardy . Weierstrass's non-differentiable function. Trans. Amer. Math. Soc. 17 (1916), 301325.

[9]J. L. Kaplan & J. A. Yorke . Chaotic behavior of multidimensional difference equations. In Functional Differential Equations and Approximation of Fixed Points (H. O. Peitgen and H. O. Walther , eds.). Springer Verlag Lecture Notes in Math #730 (1979), 228237.

[11]F. Ledrappier . Some relations between dimension and Lyapunov exponents. Commun. Math. Phys. 81 (1981), 229238.

[13]J. Moser . On a theorem of Anosov. J. Differential Equations 5 (1969), 411490.

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