Put $a_{0}= \pi/2$ and $a_{n}=\sin(a_{n-1})$.
Is $\sum a_{n}$ a convergent series?
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1$\begingroup$ What are your thoughts? $\endgroup$– SiminoreApr 10, 2017 at 7:52
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$\begingroup$ @Siminore Thank you for your edit. I have no idea for this series. But this question can introduce the following concept in non hyperbolic fixed points of maps (Then can be adapted for flows): WLOG we may assume that the fixed point of a function $f$ is $0$. We say $0$ is a conditionally fixed point if for every $p$ in a small neighborhood of $0$ $\sum f^{n} (p)$ converges. Of course this is the case for hyperbolic attractors.one can even think about the generalization for dynamics an arbitrary [en.wikipedia.org/wiki/Affine_manifold] (affine manifolds) $\endgroup$– Ali TaghaviApr 10, 2017 at 8:37
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2$\begingroup$ Duplicate of artofproblemsolving.com/community/… $\endgroup$– Jack D'AurizioApr 10, 2017 at 8:42
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3$\begingroup$ Possible duplicate of Does $\sum a_n$ converge if $a_n = \sin( \sin (...( \sin(x))...)$ $\endgroup$– Claude LeiboviciApr 10, 2017 at 8:43
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$\begingroup$ en.wikipedia.org/wiki/Affine_manifold $\endgroup$– Ali TaghaviApr 10, 2017 at 8:43
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