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.
Original language | English (US) |
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Pages (from-to) | 261-276 |
Number of pages | 16 |
Journal | Journal of Statistical Physics |
Volume | 85 |
Issue number | 1-2 |
DOIs | |
State | Published - Oct 1996 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Keywords
- Circle homeomorphism
- Critical curve
- Fractal dimension
- Invariant measure
- Renormalization
- Rotation number
- Thermodynamic formalism
- Twist map