# Tagged Questions

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### Periodic orbits

Let $x\in\mathbb R$ be a periodic point with lenght 2 of the recursion $x_{n+1}=f(x_n)$ My book about Dynamic systems says that this recursion has a fixed point now, because a periodic point with ...
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### Fixed Point of a complex dynamical spiral system

Last semester I finished my first class on complex variables and of course we had to show that $i^i$ was real. That got me wondering about quantities like $i^{i^i}$ and similar power towers. For my ...
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### Implicit Function theorem and Bifurcation points

So let us say we have a function $\dot{x} = f(x,r)$ that has some critical point at $(x_0,r_0)$ such that $f(x_0,r_0)=0$. The question now is: when is this a bifurcation point? I understand that ...
Let $f(z)$ be an entire function that is not a polynomial of degree 1 or degree 0 , where $z$ is a complex number. Let $f(z,1) = f(z)$ and let $f(z,n) = f(f(z,n-1))$. Let $g(f,1)$ be the amount of ...
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 &= ...