On real analogues of the Poincaré series

Abstract

There exist several equivalent equations for the Poincaréseries of a collection of valuations on the ring of germs offunctions on a complex analytic variety. We give defini-tions of the Poincaré series of a collection of valuationsin the real setting (i.e., on the ring of germs of functionson a real analytic variety), compute them for the case ofone curve valuation on the plane and discuss some oftheir properties.