43
votes
1answer
1k 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 $$(f\circ g)(x):=g(f(x)),$$ and with $e(x)=x$, the inverible functions even seem to form ...
3
votes
1answer
155 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 &= ...