Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 action $$\int_\gamma L(q,\dot q)\,dt$$ locally. The nondegeneracy means that the second variation restricted as a finite dimensional matrix is not degenerate.

If we do not assume the "mechanical", there are many examples having elliptic minimizing periodic orbits.

One example is the Lagrangian periodic orbit in three body problem. For some choice of parameters (mass, eccentricity), the orbit can be elliptic. It is also action minimizing as shown by Venturelli. However, if we reduce the angular momentum conservation, the system is not mechanical.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.