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

## TL;DR

This paper investigates a family of 2D piecewise linear maps, demonstrating the existence of parameter intervals with multiple renormalizations and numerous coexisting strange attractors, extending classical 1D tent map results.

## Contribution

It proves the existence of parameter intervals with multiple renormalizations and coexisting strange attractors in a 2D map family, generalizing classical 1D dynamics.

## Key findings

- Existence of parameter intervals with n-times renormalizable maps.
- Presence of at least 2^n coexisting strange attractors.
- Extension of 1D tent map dynamics to 2D maps.

## 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.