Homotopy Invariants of Time Reversible Periodic Orbits I. Theory

We introduce a family of homotopy invariants degn(γ),n=1, 2, 3, … associated to a reversible periodic orbitγof a time reversible system. We present two results: (i) we compute degn(γ) from information on the Floquet multipliers ofγ, (ii) conversely, we recover any Floquet multipliers ofγon the unit circle from the sequence degn(γ).