All Questions

Is there a polynomial Hamiltonian $H:\mathbb{R}^{4}\to \mathbb{R}$ such that the number of nontrivial periodic orbits of the corresponding Hamiltonian vector field $X_{H}$ is finite but different ...

Consider $\Bbb{R}^2$ with the usual symplectic form $$\omega = dx \wedge dy$$ For a function $H \colon \Bbb{R}^2 \to \Bbb{R}$, let $X_H$ be the Hamiltonian vector field. Then the map $\Bbb{R}^2 \to \...

It is well-known that an analytic near-identity map $\bar{x} = F_{\epsilon}(x) = x + \epsilon f(x) + O(\epsilon^{2})$ may be embedded into the flow of a differential equation, and if that map is ...

Consider mechanical Hamiltonian system of the form $$H(p,q)=\dfrac{\Vert p\Vert^2}{2}+V(q),\quad (q,p)\in T^*\mathbb T^n.$$ Here we suppose the periodic orbit $\gamma$ minimizes the Lagrangian ...

Consider a Hamiltonian, non-linear, dynamical system associated to $H(\vec{q},\vec{p})$. Assume that the number of effective degrees of freedom is relatively small, say $D=3,4,5$. Now choose a certain ...