A formula for the boundary of chaos in the lexicographical scenario and applications to the bifurcation diagram of the standard two parameter family of quadratic increasing-increasing Lorenz maps

Figure 1.  Picture of the Topological Entropy

Figure 2.  Bubble $B(\underline{0}, \underline{1})$

Figure 3.  Region $B_1(\underline{0}, 00\underline{10}, 11\underline{01}, \underline{1})$

Figure 4.  Region $B_2(00\underline{10}, \underline{01}, 11\underline{01}, \underline{1})$

Figure 5.  Region $B_3(\underline{0}, 00\underline{10}, \underline{10}, 11\underline{01})$

Figure 6.  Region $B_1 \cup B_2 \cup B_3$

Figure 7.  Region $C_1 \cup C_2 \cup C_3$

Figure 8.  Region B(a)

Figure 9.  The standard quadratic family

Figure 10.  Graph of the equation $-\mu = y(\nu)$

Figure 11.  Graph of the equation $\nu = x(\mu)$

Figure 12.  Transversal intersection at $(2, 2)$

Figure 13.  Quadratic family for $ \mu = \nu = 2$

Figure 14.  $F_{\mu, \nu}$ for $ \nu = \sqrt{\mu}$ and $ \mu = \dfrac{1+\sqrt{1+4\nu}}{2}$

Figure 15.  Intersection of the curves $\nu = \sqrt{\mu}$ and $ \mu = \dfrac{1+\sqrt{1+4\nu}}{2}$

Figure 16.  Graph of map $F_{\mu_1, \nu_1}$

Figure 17.  Graph of map $F_{(\mu_n, \nu_n)}$

Figure 18.  Graph of the map $F_{(\mu, \nu)}$ for $-\mu < -\dfrac{1+ \sqrt{1+4 \nu}}{2} $

Figure 19.  Graph of the map $ F_{ \mu(t), 0}(x)$

Figure 20.  Graph of map $F_{\mu(t), \nu}, \, 0 \leq t < \nu^2$

Figure 21.  Graph of map $F_{(\mu(t), \sqrt{t})}$