Alcuni aspetti di dinamica non lineare con applicazioni in dinamica dei fasci

With the new generation of superconducting accelerator machines, like the planned Large Hadron Collider, the beam dynamics will be dominated by nonlinear effects induced by the magnetic field errors. \\ Those nonlinear effects are potentially harmful for the operation of the machine, as they could generate particle losses in the superconducting magnet and therefore induce quenches. \\ Three main problems are discussed in this dissertation: \begin{itemize} \item The computation of the stability domain for Hamiltonian maps in two-dimensions. \item The compensation of the nonlinear effects due to the magnetic errors using analytical techniques like normal Forms analysis. \item The analysis of transport phenomena induced by slow modulation of the linear parameters of the accelerator. \end{itemize}