I report in this thesis a detailed study of the periodic oscillations detected during neutron star X-ray bursts, in low mass X-ray binaries. The properties of the interiors of neutron stars can be probed by constraining the equation of state, by determining their masses and radii. I present methods to detect and process these oscillating trains, their time properties and energy dependence. Using data from three bursting neutrons stars observed with the Rossi X-ray Timing Explorer/Proportional Counter Array, I analyzed all the detected oscillations during type 1 X-ray bursts and one superburst.I then selected the time intervals of the light curves with the most significant oscillation detection, in order to build a catalog of mean pulse profiles. Oscillation waveforms usually differ from one burst to another, because many parameters can affect them. I then elaborated a model of a rotating hotspot on the rapidly spinning surface of the neutron star. It includes the whole star, spot and geometry parameters affecting the shape of the oscillations, in an adequate relativistic pattern describing the altered space-time around the compact object. The energy dependence of the oscillation profiles confirmed that harder profiles arrive on average before softer ones for a sample of observations, as expected from the hotspot model. Finally, I fitted the waveforms and used the Monte Carlo Markov chains to derive measurements on the mass and the radius of the star. The uncertainties were too large to provide interesting constraints with current instrument capabilities, but by simulating larger collecting area, as proposed for future observatories, showed very promising results.
