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13
votes
0answers
199 views
What is the algebraic structure of functions with fixed points?
So I just noticed that the set of functions with a fixed point
$$f(x_0)=x_0,$$
are closed under composition
$$(f*g)(x):=g(f(x)),$$
and with $e(x)=x$, the inverible functions even seem to form a ...
3
votes
1answer
140 views
Fixed point: a consequence of symmetry?
I'm studying a dynamical system with $\mathbf{D}_{3}$ symmetry (the symmetry group of an equilateral triangle), which is given by:
$\begin{align*}
d\mathbf{x}_{0}/dt &= ...
