Measure of the chaotic domain in simple Hamiltonian systems Carles Sim\'o Slides of a talk given at the conference on Hamiltonian Perturbation Theory: Separatrix Splitting, Theory and Applications, held in the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, 5 to 9 May 2014. Abstract Many phenomena are described using a Hamiltonian formulation}. Integrable cases can be useful approximations. There are methods to detect the lack of integrability: either algebraic or analyic or based on numerical evidences. A key point is: which is the amount of chaos in a given system? If small (below some threshold) perhaps it can be neglected for practical applications. If it is large perhaps it takes so long to show up that one exceeds the time of validity of the model. Some crucial questions are: a) Which are the dynamical objects responsible for the chaos? b) Can they be detected and measured in~some~reasonable~way, to be able to predict the amount of chaos of the system? c) How do the answers to these questions depend on the level of energy and on the parameters of the system? The goal of the talk is to provide some answers to these questions.