Resonance in PSR B1257+12 Planetary System
  In this paper we present a new method that can be used for analysis of time of arrival of a pulsar pulses (TOAs). It is designated especially to detect quasi-periodic variations of TOAs. We apply our method to timing observations of PSR B1257+12 and demonstrate that using it it is possible to detect not only first harmonics of a periodic variations, but also the presence of a resonance effect. The resonance effect detected, independently of its physical origin, can appear only when there is a non-linear interaction between two periodic modes. The explanation of TOAs variations as an effect of the existence of planets is, till now, the only known and well justified. In this context, the existence of the resonance frequency in TOAs is the most significant signature of the gravitational interaction of planets. 
Maciej Konacki, Andrzej J. Maciejewski and Alex Wolszczan (Torun   Centre for Astronomy)