# Tagged Questions

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### Quick estimate of attractor of non-linear dynamical system [closed]

Say I have a system of form $$\frac{dy}{dt} = f(y),$$ and it is know this system has an attractor. Can I quickly for given $\varepsilon$ guess some point, such in its $\varepsilon$- neighbourhood ...
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### A question of Erdős on equidistribution

In his book Metric Number Theory, Glyn Harman mentions the following problem he attributes to Erdős: Let $f(\alpha)$ be a bounded measurable function with period 1. Is it true that ...
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### Is there a notion of “Morse index” for geodesics in a manifold with indefinite metric that is well-behaved under cutting and gluing?

More generally, I'm interested in the situation of Lagrangian mechanics. And actually my question is local, so you can work on $\mathbb R^n$ if you like. I will begin with some background on ...
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### Dropping three bodies

Consider the usual three-body problem with Newtonian $1/r^2$ force between masses. Let the three masses start off at rest, and not collinear. Then they will become collinear a finite time ...
Let the sequence $u_1, u_2, \ldots$ satisfy $u_{n+1} = u_n - u_n^2 + O(u_n^3)$. Then it can be shown that if $u_n \to 0$ as $n \to \infty$, then $u_n = n^{-1} + O(n^{-2} \log n)$. (See N. G. de ...