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In this thesis I present most of the results obtained during my PhD, where Iworked on different subjects regarding jamming in systems of frictionlessspheres. In particular, I focused on microscopic properties of jammed packings,such as the distribution of contact forces and interparticle gaps, as well asthe single particle dynamics that occur near the jamming point. Several ofthese results have already been presented in Refs. [1,2], but here I include amore detailed analysis of some of them. Besides, all the results of the secondchapter are new, even if related to such works.

Numerical study of the microscopic structure of jammed systems: from inferring their dynamics to finite size scaling