Lev LERMAN

Research nstitute for Applied Mathematics.&.Cybern.
10..Ul'yanovSt.,
Nizhny Novgorod 603005 
RUSSIA
lerman@focus.nnov.ru

Hyperbolic and elliptic behavior in Hamiltonian systems with saddle-foci or saddle-centers

Abstract: Last results concerning orbit structure in Hamiltonian systems with two and more degrees of freedom having homoclinic orbits and heteroclinic contours to saddle-focus or saddle-center equilibriums will be discussed. This includes hyperbolic subsets and their description by means of symbolic dynamics continuously depending on Hamiltonian levels and parameters, tangencies of separatrix manifolds and related creation of elliptic periodic orbits, other bifurcational phenomena in such systems. Applications of results obtained to systems from different branches of physics will be pointed out.