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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.

We introduce the concept of *Expanding Baker Maps* and *renormalizable Expanding Baker Maps* in a two-dimensional scenario. For a one-parameter family of *Expanding Baker Maps* we prove the existence of an interval of parameters for which the respective transformation is *renormalizable*. Moreover, we show the existence of intervals of parameters for which coexistence of strange attractors takes place.

We characterize the attractors for a two-parameter class of two-dimensional piecewise affine maps. These attractors are strange attractors, probably having finitely many pieces, and coincide with the support of an ergodic absolutely invariant probability measure. Moreover, we demonstrate that every compact invariant set with non-empty interior contains one of these attractors. We also prove the existence, for each natural number $ n, $ of an open set of parameters in which the respective transformation exhibits at least $ 2^n $ non connected two-dimensional strange attractors each one of them formed by $ 4^n $ pieces.

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