Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems

Using recent results on measure theory and algebraic geometry, we show how semidefinite programming can be used to construct invariant measures of onedimensional discrete dynamical systems (iterated maps on a real interval). In particular we show that both discrete measures (corresponding to finite cycles) and continuous measures (corresponding to chaotic behavior) can be recovered using standard software, paving the way for a numerical study of probabilistic properties of dynamical systems.