MathDB

Let

(x_1,y_1) = (0.8, 0.6)

and let

x_{n+1} = x_n \cos y_n - y_n \sin y_n

and

y_{n+1}= x_n \sin y_n + y_n \cos y_n

for

n=1,2,3,\dots

. For each of

\lim_{n\to \infty} x_n

and

\lim_{n \to \infty} y_n

, prove that the limit exists and find it or prove that the limit does not exist.

Problem Statement