The Split of Separatrice Loop and Birth of Non-Degenerate Solutions with Long Period in the Case of Non-Conservative Perturbations of Hamiltonian Systems

The work is dedicated to the investigation of the connection between separatrix split and birth of the isolated periodic solutions in the perturbated Hamiltonian system with one degree of freedom. By means of H. Poincaré [1] and V.V. Kozlov [2] methods the result of [3] is generalized to the case of non-conservative perturbation. The general theorem, obtained in chapter 2, permits to arque about system's periodic solutions by value of asymptotic surfaces split. In the final part of the work, non-conservative perturbation in Duffing-type equation serves as an example (see [4]).