Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors

Abstract

For a two parameter family of two-dimensional piecewise linear maps and for every natural number $n$ we prove not only the existence of intervals of parameters for which the respective maps are $n$ times renormalizable but also we show the existence of intervals of parameters where the coexistence of at least $2^n$ strange attractors takes place. This family of maps contains the two-dimensional extension of the classical one-dimensional family of tent maps.