The bifurcation locus for numbers of bounded type

Giulio Tiozzo (University of Toronto)

11-May-2021, 12:30-13:30 (3 years ago)

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

( paper | slides )


One World Numeration seminar

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