Periodic orbits of Hamiltonian systems - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T04:57:54Z http://mathoverflow.net/feeds/question/86031 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86031/periodic-orbits-of-hamiltonian-systems Periodic orbits of Hamiltonian systems McParson 2012-01-18T19:56:41Z 2012-01-19T10:43:00Z <p>Consider a second order Hamiltonian system of the type $$\ddot{x}+V'(x)=0, \quad x \in \mathbb{R}^N.$$ Under very `natural assumptions' it is possible to prove the existence of a non constant $T$-periodic orbit $\varphi^T=(\varphi_{1}^{T},\ldots,\varphi_{N}^{T})$ for any given $T>0$. If $N \ge 2$ it may as well happen that $\varphi_{i}^{T} \equiv \text{ constant }$ for some index $i$.</p> <p>Is there any result that guarantees the existence of a $\varphi^T$ for which all the components are non constant functions?</p>