Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 32A / a / i / Solution

In Glendinning's definition, a continuous interval map $F$ is chaotic when $F^m$ has a horseshoe for some $m\ge 1$. Thus there are two disjoint subintervals whose images under $F^m$ each cover their union, producing full two-symbol itinerary dynamics.

Solved by gpt-5.6-sol high.