Self-similarity of Farey Staircases
Grynberg, Sebastian ; Piacquadio, Maria N.
arXiv, 0306024 / Harvested from arXiv
Text on arXiv
We study Cantor Staircases in physics that have the Farey-Brocot arrangement for the Q/P rational heights of stability intervals I(Q/P), and such that the length of I(Q/P)is a convex function of 1/P. Circle map staircases and the magnetization function fall in this category. We show that the fractal sets Ommega underlying these staircases are connected with key sets in Number Theory via their (alpha,f(alpha)) multifractal decomposition spectra. It follows that such sets Ommega are self similar when the usual (Euclidean) measure is replaced by the hyperbolic measure induced by the Farey-Brocot partition.
Publié le : 2003-06-09
Classification:  Mathematical Physics,  11K55 
@article{0306024,
     author = {Grynberg, Sebastian and Piacquadio, Maria N.},
     title = {Self-similarity of Farey Staircases},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306024}
}

Grynberg, Sebastian; Piacquadio, Maria N. Self-similarity of Farey Staircases. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306024/