Resonance in PSR B1257+12 planetary system

In this paper we present a new method that can be used for analysis of time s of arrival (TOAs) of pulsar pulses. It is especially designed to detect q uasi-periodic variations of TOAs. We apply our method to timing observation s of PSR B1257+12 and demonstrate that by using it, it is possible to detec t not only first harmonics of a periodic variations, but also the presence of a resonance effect. The resonance effect detected independently of its p hysical origin can appear only when there is a nonlinear interaction betwee n two periodic modes. The explanation of TOAs variations as an effect of th e existence of planets was, until now, the only known and well-justified ex planation. In this context, the existence of the resonance frequency in TOA s is the most significant signature of the gravitational interaction of pla nets.