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In Cushman and Bates, Global Aspects of Classical Integrable Systems, 1997, I have read In a widely circulated but unpublished letter in 1965, Palais explained the symplectic formulation of Hami …

Let us assume someone is interested in the study of Hamiltonian mechanics. What are good examples to illustrate him of the usefulness of contact geometry in this context? On one hand the Hamiltonian …

I do not know if this question is appropriate for this site, but I posted here without having answers, so now I make this attempt. Let be $(M,g)$ a pseudoriemannian manifold. Let us identify the tan …

I am not totally sure if this question is appropriate for MathOverflow, or if it more adeguate to MathStackexchange. As usual any feedback is welcome. Introduction Given an arbitrary smooth manifold $ …

Studying the Hamilton-Jacobi equation, I meet a generalization of the notion of its solutions, which is found already in the work of Sophus Lie. For an H-J eqn, I mean a first order pde $H\circ dS …

I posted this question here on math.stackexchange.com. I have not had an answer, and I thought it could be more appropriate here. (Please, If you judge this my opinion is wrong, then I will delete thi …

Disclaimer: The original question consisted of two parts. The first one has been answered negatively (see below the answers of Sam Lisi and Alejandro). It remains the second one. Background …

Given a Poisson manifold $(P,\{\cdot,\cdot\})$, its characteristic distribution $\mathcal C$ is the singular tangent distribution on $M$ generated by the Hamiltonian vector fields,i.e. $$\mathcal C=\o …

Context According to Arnol'd, a contact structure on a smooth manifold $M$ is given by a corank 1 tangent distribution $C$ which is maximally non-integrable; this means that, for any local $1$-form …

The hamiltonian flow box theorem, as stated in Abraham and Marsden's Foundations of Mechanics, says that: Given an hamiltonian system $(M,\omega,h)$ with $dh(x_0)\neq 0$ for some $x_0$ in $M$, there …

My question is: Are the orbits of the geodesic flow on $S^n$ determined as the fibers of the momentum map for its $SO(n+1)$ symmetry? I started by considering the analog problem for the orbits of the …

Is there some reference where the existence of local generalized action-angle variables is discussed in some detail for concrete examples of hamiltonian systems of mechanical type? After Dazord and D …

On a manifold $M$, let $\mathcal F$ be a foliation having even-dimensional orientable leaves. I was wondering under what hypothesis I can state that $\mathcal F$ is the symplectic foliation of a Poiss …

Reading a paper on hamiltonian mechanics, in a section on classical examples of complete integrability, it is examined the geodesic flow of a triaxial ellipsoid. Before separating the variables in th …

Reading about the geometrical theory of systems of first order pdes, I have met a result from symplectic geometry, that is easy to prove, but I am unable to give a reference for it. So my question is …