SIMBAD references

We present a possible evolutionary scenario for the AM Her binaries to explain the orbital period distribution with the fact that several AM Her's have been recently found inside the 2-3h period gap. We show that in the gap, the evolution (driven by the gravitational wave radiation) is influenced by the X-ray heating. A variable X-ray heating keeps the secondary in contact with its Roche lobe, while the system is evolving (and accreting) through the period gap. Hard X-ray radiation penetrates deep inside the secondary and a significant fraction of the incident flux is released in the convective zone of the secondary's facing hemisphere. This allows a spherical heating, provided that the circulation time scale is smaller than the evolutionary one. In the gap this is probably the case, although detailed numerical computations will be needed. Contact binaries of W UMa type serve an example of late type binary systems where observational data show the spherical heating to work.