Kybernetika 48 no. 6, 1089-1099, 2012

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

Didier Henrion


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.


invariant measures, semidefinite programming, dynamical systems


37-04, 37L40, 90C22


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