The Abdus Salam International Centre for Theoretical Physics (ICTP) is organizing a "School and Conference in Dynamical Systems". The activity will be held from 20 July to 7 August 2015, in Trieste, Italy. It will be directed by S. Luzzatto (ICTP, Trieste, Italy), M. Viana (IMPA, Rio de Janeiro, Brazil) and J.-C. Yoccoz (Collège de France, Paris, France). TOPICS • Chaotic dynamics: homoclinic bifurcations, attractors, generic systems, partial hyperbolicity and dominated splitting, Lorenz attractors. • Conservative dynamics: KAM and Aubry-Mather theories, diffusion in Hamiltonian systems, billiards, infinite dimensional systems, celestial mechanics. • Ergodic Theory: Sinai-Ruelle-Bowen measures, stochastic stability, Lyapunov exponents, linear cocycles, spectral theory of Schrodinger operators, recurrence and applications to Number Theory. • Geometric, algebraic, and topological aspects of Dynamics: smooth group actions, knots and braids, commutators. • One-dimensional dynamics: density of hyperbolicity, parametrized families of transformations, stochastic versus regular behavior. During the two first weeks (20-31 July): courses on the following topics will be delivered: Applications of homogeneous dynamics: from number theory to statistical mechanics Jens Marklof (University of Bristol)/ Andreas Strömbergsson (Uppsala University) Renormalization in low dimensional dynamics Marco Martens (SUNY at Stony Brook) Partially hyperbolic diffeomorphisms Sylvain Crovisier (Université Paris 13)/ Rafael Potrie (CMAT) The second and third week will be a conference. The invited speakers will include some of the best experts in the field as well as brillant young researchers. They will provide the participants with some of the most recent and most interesting perspectives for future research.