Attractors of dual continued fractions
| Autor: | Panti, Giovanni |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a Farey-type map F with full branches in the extended Hecke group Gamma_m, its dual F_# results from constructing the natural extension of F, letting time go backwards, and projecting. Although numerical simulations may suggest otherwise, we show that the domain of F_# is always tame, that is, it always contains intervals. As a main technical tool we construct, for every m=3,4,5,..., a homeomorphism M_m that simultaneously linearizes all maps with branches in Gamma_m, and show that the resulting dual linearized iterated function system satisfies the strong open set condition. We explicitly compute the Holder exponent of every M_m, generalizing Salem's results for the Minkowski question mark function M_3. Comment: 23 pages. Example 4.5 slightly modified and other minor corrections. To appear in the J. of Number Theory |
| Databáze: | arXiv |
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