Abstract : The topic of this thesis is the study of beam dynamics in storage rings with a restriction to single particle transverse dynamics. In a first part, tools (Frequency Map Analysis, Hamiltonian, Integrator) are presented for studying and exploring the dynamics. Numerical simulations of four synchrotron radiation sources (the ALS, the ESRF, SOLEIL and Super-ACO) are performed. We construct a tracking code based on a new class of symplectic integrators (Laskar and Robutel, 2000). These integrators with only positive steps are more precise by an order of magnitude than the standard Forest and Ruth's scheme. Comparisons with the BETA, DESPOT and MAD codes are carried out. Frequency Map Analysis (Laskar, 1990) is our main analysis tool. This is a numerical method for analysing a conservative dynamical system. Based on a refined Fourier technique, it enables us to compute frequency maps which are real footprints of the beam dynamics of an accelerator. We stress the high sensitivity of the dynamics to magnetics errors and sextupolar strengths.
The second part of this work is dedicated to the analysis of experimental results from two light sources. Together with the ALS accelerator team (Berkeley), we succeeded in obtaining the first experimental frequency map of an accelerator. The agreement with the machine model is very impressive. At the Super-ACO ring, the study of the tune shift with amplitude enabled us to highlight a strong octupolar-like component related to the quadrupole fringe field. The aftermaths for the beam dynamics are important and give us a better understanding the measured ring performance. All these results are based on turn by turn measurements. Many closely related phenonema are treated such as response matrix analysis or beam decoherence.