 Odd quadratic Lorenz map

Away from zero this discontinuous map is odd, and its branch derivatives are $2|x|$. With the convention $\mathrm{sgn}(0)=1$, its value at zero is $-\mu$, so it is not odd at zero unless $\mu =0$. A global transition at $\mu =0$ turns two small stable fixed points into one stable symmetric two-cycle. Its unsigned dynamics can be related to the even quadratic map $g_{\mu }(x)=\mu -x^2$, provided critical hits are treated separately.

// Target: dynamical-systems.bigb