Geodesic
Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
Kybernetika, Tome 48 (2012) no. 6, pp. 1089-1099.

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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.
Classification : 37-04, 37L40, 90C22
Keywords: dynamical systems; invariant measures; semidefinite programming 
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     author = {Henrion, Didier},
     title = {Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems},
     journal = {Kybernetika},
     pages = {1089--1099},
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     number = {6},
     year = {2012},
     mrnumber = {3052875},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_6_a1/}
}
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Henrion, Didier. Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems. Kybernetika, Tome 48 (2012) no. 6, pp. 1089-1099. http://geodesic.mathdoc.fr/item/KYB_2012__48_6_a1/