11 citations · 17 across the 5 of their papers we have counts for
5 papers
Continuous self-similarity in parametric piecewise isometries
John H Lowenstein, Franco Vivaldi
We exhibit two distinct renormalization scenarios in many-parameter families of piecewise isometries (PWI) of a rhombus. The rotational component, defined over the quadratic field…
Renormalization of a one-parameter family of piecewise isometries
John H. Lowenstein, Franco Vivaldi
We consider a one-parameter family of piecewise isometries of a rhombus. The rotational component is fixed, and its coefficients belong to the quadratic number field $K=\mathbb{Q}(…
Approach to a rational rotation number in a piecewise isometric system
John H. Lowenstein, Franco Vivaldi
We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure…
Geometric representation of interval exchange maps over algebraic number fields
G. Poggiaspalla, J. H. Lowenstein, F. Vivaldi
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and…
Scaling dynamics of a cubic interval exchange transformation
J. H. Lowenstein, F. Vivaldi
We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes…