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| | [No title] (Site not responding. Last check: 2007-11-07) |
 | | We discuss the renormalization flow on the basis of the continued fraction expansion of the frequency. |
| | This accumulation motivates the setup of a renormalization transformation combining a {\em rescaling} of phase space and an {\em elimination} of the irrelevant part at each scale.\\ An attractive ({\em trivial}) fixed point of the renormalization represents the phase where the torus exists. |
| | The renormalization $\mathcal{R}_{a_{s-1}} \mathcal{R}_{a_{s-2}}\cdots\mathcal{R}_{a_0}$ changes $\o=[a_0,a_1,\ldots]$ into $[a_s,a_{s+1},\ldots]$, and $\alpha$ into $[a_{s-1},a_{s-2},\ldots,a_0, b_0,b_1,\ldots]$.\\ If $\o$ has a periodic continued fraction expansion of period $s$, i.e., $\o=[(a_1,\ldots,a_s)_\infty]$, one expect to have a nontrivial fixed point on the critical surface of the renormalization transformation in which one step is defined by the composition $\mathcal{R}_{a_s} \mathcal{R}_{a_{s-1}}\cdots\mathcal{R}_{a_1}$. |
| www.ma.utexas.edu /mp_arc/papers/98-626 (2259 words) |
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