Families of periodic orbits in resonant reversible systems

摘要

We study the dynamics near an equilibrium point p(0) of a Z(2)(R)- reversible vector field in R-2n with reversing symmetry R satisfying R-2 = I and dim Fix (R) = n. We deal with one-parameter families of such systems X-lambda such that X-0 presents p(0) a degenerate resonance of type 0: p: q. We are assuming that the linearized system of X-0 (at p(0)) has eigenvalues: lambda(1) = 0 and lambda(j) = +/- i alpha(j), j = 2,...n. Our main concern is to find conditions for the existence of one-parameter families if periodic orbits near the equilibrium.