Geodesic
Renormalization on the one-dimansion torus
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 142-154 
N. N. Manuylov. Renormalization on the one-dimansion torus. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 142-154. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a8/
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     title = {Renormalization on the one-dimansion torus},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a8/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Renormalization formulas connecting the points of the orbits $O^\pm_0$, i.e., the sequences generated by an irrational shift on the half-open interval $[0,1)$ or $(0,1]$, and the points of the orbits' derivatives $d^mO^\pm_0$, i.e., the sequences obtained by restricting $O^\pm_0$ to half-open intervals of smaller length, are obtained.

[1] V. G. Zhuravlev, “Odnomernye razbieniya Fibonachchi”, Izv. RAN, ser. matem., 2004 (to appear)

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