11 citations · 15 across the 2 of their papers we have counts for
2 papers
math.DS2009★ 4 cited
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…
math.DS2007★ 11 cited
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…