EDB — 0DK

Exercises

1. [0DK]Let \(f(x)=x-x^ 3\) and \(x_ 0∈{\mathbb {R}}\), and \((x_ n )_{n∈{\mathbb {N}}}\) a sequence defined by recurrence by \(x_{n+1}=f(x_ n)\). Prove that there is a \(𝜆{\gt}0\) such that if \(|x_ 0|{\lt}𝜆\) then \(x_ n→ 0\), while if \(|x_ 0|{\gt}𝜆\) then \(|x_ n|→ ∞\); and possibly calculate this \(𝜆\).

   Solution 1

   [0DM]↺↻