Lozi map embedded into the 2D border collision normal form

A 2D piecewise linear continuous two-parameter map known as the Lozi map is a special case of the 2D border collision normal form depending on four parameters. In the present paper, we investigate how the bifurcation structure of the Lozi map is incorporated into the bifurcation structure of the 2D border collision normal form using an analytical representation of the boundaries of the largest periodicity regions related to the cycles with rotation number 1/n, n= 3. At the centre bifurcation boundary of the stability domain of the fixed point both maps are conservative which leads to a quite intricate bifurcation structure near this boundary.

Automated summary

In this paper, the bifurcation structure of the Lozi map, a 2D piecewise linear continuous two-parameter map, is investigated and compared to the 2D border collision normal form. By analyzing the boundaries of the largest periodicity regions related to cycles with rotation number 1/n (n=3), the bifurcation structure of the Lozi map is incorporated into the 2D border collision normal form. Both maps exhibit intricate bifurcation structures near the center bifurcation boundary of the stability domain of the fixed point due to their conservative nature.