Cascades of reversible homoclinic orbits to a saddle-focus equilibrium

In a reversible system, we consider a homoclinic orbit being bi-asymptotic to a saddle-focus equilibrium. As was proved by Devaney (1977), there exists a one-parameter family of periodic orbits accumulating onto this homoclinic orbit. In the present paper, we show that for any n greater than or equal to 2 there exist infinitely many n-homoclinic orbits in a neighborhood of the primary homoclinic orbit. Each of them is accompanied by one or more families of periodic orbits. Moreover, we indicate how these families of periodic orbits correspond to branches of subharmonic periodic orbits.