7 citations · 9 across the 2 of their papers we have counts for
3 papers
math.DS2023
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…
math.DS2014★ 2 cited
Growth of heights in piecewise-affine planar maps
John A. G. Roberts, Franco Vivaldi
We consider the growth of heights of the points of the orbits of (piecewise) affine maps of the plane, with rational parameters. We analyse the asymptotic growth rate of both globa…
math.DS2012★ 7 cited
Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
Michael Baake, Natascha Neumaerker, John A. G. Roberts
We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit s…