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Brian R. Hunt, Konstantin M. Khanin, Yakov G. Sinai, and James A. Yorke

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J. Stat. Phys. 85 (1996), 261-276.
*

We examine the dimension of the invariant measure for some singular
circle homeomorphisms for a variety of rotation numbers, through both
the thermodynamic formalism and numerical computation. The maps we
consider include those induced by the action of the standard map on
an invariant curve at the critical parameter value beyond which the
curve is destroyed. Our results indicate that the dimension is
universal for a given type of singularity and rotation number, and
that among all rotation numbers, the golden mean produces the largest
dimension.

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*Last updated: May 31, 1998*