Questions tagged [periodic-orbit]

In this question a nontrivial periodic orbit is a periodic orbit which is not a singular point. Let $p: \mathbb{R}^n \to \mathbb{R}$ be a ...

Let $X$ be a compact metric space and $f:X\to X $ homeomorphism. Let $V:X\to \mathbb{R}$ be a Lyapunov function for $(X,f)$ (continuous function such that $(\forall x\notin Fix(f))\ \ V(f(x))<V(x))...

I wonder whether all (composites of) trigonometric and inverse trigonometric functions with periodic functional iterations can be found. In order to specify what I mean by that, let's introduce some ...

Let $v\in\mathcal{C}^1(\mathbb{R}^n,\mathbb{R}^n)$ $(n\geq 2)$ a vector field, such that the set $E=\{v=0\}$ is a manifold of dimension $n-2$. Assume that for every $x\in\mathbb{R}^n-E$, the ...

First, a contact form $\alpha$ on $M$ with Reeb vector field $R$ is said to be non-degenerate if, for any point $p$ such that $\phi_T^R(p) = p$, we have $\det{(\textrm{id}_{T_pM} - (d \phi_T^R)_p)} \...

The following is about getting help for a proof on existence and indexability of periodic points of the exponential-function, here with base $e:=\exp(1)$. Update The question is a complete rewriting ...