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Strange behavior of $x_{n+1}=x_n +\lambda \sin x_n$
Consider a sequence $(x_n)$ satisfying $x_{n+1}=x_n +\lambda \sin x_n$.
You would expect the sequence $x_n$ to depend on $x_0$ and to exhibit a chaotic, Brownian-type behavior, and indeed it does ...
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Do these rational sequences always reach an integer?
This post comes from the suggestion of Joel Moreira in a comment on An alternative to continued fraction and applications (itself inspired by the Numberphile video 2.920050977316 and Fridman, ...
