Communications in Mathematical Physics

, Volume 320, Issue 1, pp 101–119 | Cite as

Dimensions of Attractors in Pinched Skew Products



We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.


Lyapunov Exponent Invariant Measure Hausdorff Dimension Global Attractor Hausdorff Measure 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversität BremenBremenGermany
  2. 2.Department of MathematicsTU DresdenDresdenGermany

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