The bifurcation locus for numbers of bounded type
| Autor: | Giulio Tiozzo, Carlo Carminati |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics Dynamical Systems (math.DS) Bounded type Null set Bifurcation locus Dimension (vector space) Bounded function 11A55 37C45 37E05 37E20 11J06 FOS: Mathematics Mathematics - Dynamical Systems Continued fraction Bifurcation Mathematics Unit interval |
| Popis: | We define a family B(t) of compact subsets of the unit interval which generalizes the sets of numbers whose continued fraction expansion has bounded digits. We study how the set B(t) changes as one moves the parameter t, and see that the family undergoes period-doubling bifurcations and displays the same transition pattern from periodic to chaotic behavior as the usual family of quadratic polynomials. The set E of bifurcation parameters is a fractal set of measure zero and Hausdorff dimension 1. We also show that the Hausdorff dimension of B(t) varies continuously with the parameter, and the dimension of each individual set equals the dimension of a corresponding section of the bifurcation set E. 32 pages, 2 figures. Accepted version in Ergodic Th. Dynam. Systems |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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