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

Didier Henrion (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

Using recent results on measure theory and algebraic geometry, we show how semidefinite programming can be used to construct invariant measures of one-dimensional 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.

Mots clés: dynamical systems; measure theory; semidefinite programming

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion. Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems. Kybernetika, 2012, 48 (6), pp. 1089-1099. ⟨hal-00666098⟩