Fractal properties of critical invariant curves |
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| Authors: | Brian R Hunt Konstantin M Khanin Yakov G Sinai James A Yorke |
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| Institution: | (1) Institute for Physical Science and Technology, University of Maryland, 20742 College Park, Maryland;(2) Department of Mathematics, Princeton University, 08544-1000 Princeton, New Jersey;(3) Landau Institute of Theoretical Physics, Russian Academy of Sciences, 117334 Moscow, Russia |
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| Abstract: | 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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| Keywords: | Thermodynamic formalism fractal dimension invariant measure circle homeomorphism rotation number twist map critical curve renormalization |
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