Dissipative Hamiltonian System with a Periodic Force - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T03:41:14Z http://mathoverflow.net/feeds/question/78698 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78698/dissipative-hamiltonian-system-with-a-periodic-force Dissipative Hamiltonian System with a Periodic Force hoj201 2011-10-20T19:51:33Z 2011-10-20T19:51:33Z <p>Let $H:P \to \mathbb{R}$ be a Hamiltonian on a symplectic manifold $(\omega,P)$ and let $X_H: P \to TP$ be the Hamiltonian vector-field. Let $F:P \to T^*P$ be a dissipative force field such that for $Y = \omega^{\sharp}(F)$ we have that $Y[H] &lt; 0$ everywhere outside a point $x_0 \in P$. This makes $x_0$ a stable point of the dissipative Hamiltonian system $(P,\omega,H,F)$. Now let $f: \mathbb{R} \times P \to T^*P$ be a time-periodic force. My question: Does there exists a periodic orbit (near $x_0$) for the periodically forced system $(P,\omega,H, F + \epsilon f)$ for sufficiently small $\epsilon$ ? I'm sure the answer is yes, but how big can $\epsilon$ be?</p>