Families of periodic orbits in resonant reversible systems

Abstract

We study the dynamics near an equilibrium point p0 of a Z2(ℝ)-reversible vector field in ℝ2n with reversing symmetry R satisfying R2 = I and dimFix(R) = n. We deal with one-parameter families of such systems Xλ such that X0 presents at p0 a degenerate resonance of type 0: p: q. We are assuming that the linearized system of X0 (at p0) has as eigenvalues: λ1 = 0 and λj = ±iαj, j = 2, … n. Our main concern is to find conditions for the existence of one-parameter families of periodic orbits near the equilibrium.