Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit
  We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from Groves-Schneider, we show that there are many solutions which stay close to this homocline during all times. We point out that the solutions we construct are not small. 
Beno\^it Gr\'ebert (LMJL), Tiphaine J\'ez\'equel (ENS Cachan   Bretagne), Laurent Thomann (LMJL)
math.AP