Questions tagged [periodic-orbit]

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Stable periodic orbits for three equal masses

For three equal masses in any number of dimensions (this might not be important, but 2D or 3D or 4D is fine) under just classical gravity (i.e., inverse-square force law), what stable periodic orbits ...
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Is a "global period" similar to a "local period"?

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 ...
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Chain recurrent points of a gradient-like system

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))...
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Can all (inverse) trigonometric functions with periodic iterates be characterized?

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 ...
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Genericity of contact structures all of whose closed Reeb orbits are nondegenerate

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)} \...
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Exact solution to a periodic linear ODE sought

We have been studying a Hamiltonian system that possesses a one-parameter family of periodic orbits, depending on the energy level $h$. We "know" via various non-rigorous means that these ...
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Is my ansatz for finding $n$-periodic-points of the exponential-function exhaustive?

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 ...
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3 votes
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Periodic orbit for certain Hamiltonian on the tangent bundle

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 ...
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3 votes
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An elliptic operator whose corresponding symbol Hamiltonian vector field has an isolated periodic orbit

Let $D$ be a differential operator on the space of smooth functions on a manifold $M$. The symbol of $D$ can be considered as a Hamiltonian on the cotangent bundle $T^*M$. We call ...
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