Tent Branch Boundary Scan - Nonlinear Dynamics and Stability Step by Step

The tent map branch boundary is scanned around the equality row. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Below the split the tent map uses the low branch

One quarter doubles to one half on the low-or-equal branch.

2\cdot\frac{1}{4}=\frac{1}{2}

The equality row still belongs to low-or-equal

At one half the output is one, and the branch name records the equality convention.

2\cdot\frac{1}{2}=1

Past the split the high branch takes over

The right row returns to one half, so the table shows continuity without hiding the branch switch.

\begin{array}{c|c|c}x&f(x)&\text{branch}\\\frac{1}{4}&\frac{1}{2}&\text{low-or-equal}\\\frac{1}{2}&1&\text{low-or-equal}\\\frac{3}{4}&\frac{1}{2}&\text{high}\\\end{array}