Questions tagged [periodic-orbit]

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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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121 views

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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Floquet theory and Poincaré theorem on the continuation of periodic orbit

I read about the Floquet theory and a theorem that it named Poincaré's theorem of the continuation of periodic orbit. Poincaré's Theorem: Consider a dynamical system depending on the parameter $\...
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1answer
156 views

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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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 ...