= Interval exactness of a tent-map core
If $\sqrt2<s\leq2$, every nondegenerate subinterval of $A=[1-s,1]$ eventually maps onto $A$. Away from the <critical point>, lengths multiply by $s$; one fold loses at most a factor of two. If an interval and its image both contain zero, its second image is $A$. Otherwise every two steps increase length by at least $s^2/2>1$, which cannot continue inside bounded $A$. Applying the <intermediate value theorem> to an interval that covers itself then gives a <periodic point> in every subinterval.
// Target: dynamical-systems.bigb
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