Fractal properties of critical invariant curves | Zendy

Brian R. Hunt | Zendy; Konstantin Khanin | Zendy; Yakov G. Sinai | Zendy; James A. Yorke | Zendy

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Fractal properties of critical invariant curves

Author(s) -

Brian R. Hunt,

Konstantin Khanin,

Yakov G. Sinai,

James A. Yorke

Publication year - 1996

Publication title -

journal of statistical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.71

H-Index - 115

eISSN - 1572-9613

pISSN - 0022-4715

DOI - 10.1007/bf02175565

Subject(s) - singularity , mathematics , rotation number , invariant (physics) , fractal dimension , computation , fractal , mathematical analysis , invariant measure , pure mathematics , mathematical physics , algorithm , ergodic theory

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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