# Tagged Questions

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### conjecture: a supremum property of the cosine fixed point?

in a previous question a composition of circular functions was defined for each binary string of finite length. this question will use the same terminology. if the existence of a fixed point is ...
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### Brouwer's fixed-point theorem and iterative convergence of a composition of circular functions

let $\psi:[0,1]\times \{0,1\} \rightarrow [0,1]$ be defined by: $$\psi(x,\beta) = \beta \cos x + (1-\beta) \sin x$$ define $B_n$ as the set of $2^n$ binary strings $b=b_0b_1\dots b_{n-1}$ where ...
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### convergence of the iterated cosine

it can be demonstrated by elementary means that the curves $y=\cos x$ and $y=x$ meet exactly once, at a value $x=\alpha$ satisfying: $$\cos \alpha = \alpha$$ it is also evident (empirically) that ...
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### Rendezvous problem - Dynamical Systems

I'm learning about graph-based distributed control and there's a problem called "the rendezvous problem" that uses the Laplacian matrix as the state matrix of the system. I have a graph with 4 nodes ...