21 citations · 48 across the 13 of their papers we have counts for
16 papers
Bézier curves and the Takagi function
Lenka Ptackova, Franco Vivaldi
We consider Bézier curves with complex parameters, and we determine explicitly the affine iterated function system (IFS) corresponding to the de Casteljau subdivision algorithm, to…
Critical curves of rotations
John A G Roberts, Asaki Saito, Franco Vivaldi
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected…
Critical curves of a piecewise linear map
John A. G. Roberts, Asaki Saito, Franco Vivaldi
We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs…
Cauchy distributions for the integrable standard map
Anastasios Bountis, J. J. P. Veerman, Franco Vivaldi
We consider the integrable (zero perturbation) two--dimensional standard map, in light of current developments on ergodic sums of irrational rotations, and recent numerical evidenc…
On the Unboundedness of the Transit Time of Mean-Median Orbits
Jonathan Hoseana, Franco Vivaldi
The transit time of mean-median orbits ---the time it takes for an orbit to become stationary--- has been conjectured to be finite but unbounded over the rationals. Through a study…
Geometrical Properties of the Mean-Median Map
Jonathan Hoseana, Franco Vivaldi
We study the mean-median map as a dynamical system on the space of finite sets of piecewise-affine continuous functions with rational coefficients. We determine the structure of th…