ISSN:
1572-9613
Keywords:
Thermodynamic formalism
;
fractal dimension
;
invariant measure
;
circle homeomorphism
;
rotation number
;
twist map
;
critical curve
;
renormalization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02175565
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