Phase transitions on one-dimensional symbolic systems
By Tamara Kucherenko
Approximating entropy/pressure for multidimensional shifts of finite type
By Ronnie Pavlov
Appears in collections : Dynamics of evolution equations / Systèmes dynamiques et problèmes d'évolution, Exposés de recherche
These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb while controlling the dynamics: closing and connection of orbits, perturbation of the tangent dynamics... We derive various applications to the description of $C^1$-generic diffeomorphisms.