The bifurcation locus for numbers of bounded type
Giulio Tiozzo (University of Toronto)
Abstract: We define a family $B(t)$ of compact subsets of the unit interval which provides a filtration of the set of numbers whose continued fraction expansion has bounded digits. This generalizes to a continuous family the well-known sets of numbers whose continued fraction expansion is bounded above by a fixed integer.
We study how the set $B(t)$ changes as the parameter $t$ ranges in $[0,1]$, and describe precisely the bifurcations that occur as the parameters change. Further, we discuss continuity properties of the Hausdorff dimension of $B(t)$ and its regularity.
Finally, we establish a precise correspondence between these bifurcations and the bifurcations for the classical family of real quadratic polynomials.
Joint with C. Carminati.
dynamical systemsnumber theory
Audience: researchers in the topic
Series comments: Description: Online seminar on numeration systems and related topics
For questions or subscribing to the mailing list, contact the organisers at numeration@irif.fr
Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
*contact for this listing |