Geodesic
Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
Kybernetika, Tome 48 (2012) no. 6, pp. 1089-1099 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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 
@article{KYB_2012_48_6_a1,
     author = {Henrion, Didier},
     title = {Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems},
     journal = {Kybernetika},
     pages = {1089--1099},
     year = {2012},
     volume = {48},
     number = {6},
     mrnumber = {3052875},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a1/}
}
TY  - JOUR
AU  - Henrion, Didier
TI  - Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
JO  - Kybernetika
PY  - 2012
SP  - 1089
EP  - 1099
VL  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a1/
LA  - en
ID  - KYB_2012_48_6_a1
ER  - 
%0 Journal Article
%A Henrion, Didier
%T Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
%J Kybernetika
%D 2012
%P 1089-1099
%V 48
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a1/
%G en
%F KYB_2012_48_6_a1
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/