On dynamics and bifurcations of area-preserving maps with homoclinic tangencies

Amadeu Delshams, Marina Gonchenko, Sergey Gonchenko

Published 2014-07-21, updated 2015-08-04Version 2

We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits. In particular, we find conditions for such maps to have infinitely many generic (KAM-stable) elliptic periodic orbits of all successive periods starting at some number.