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

Didier Henrion

Kybernetika (2012)

  • Volume: 48, Issue: 6, page 1089-1099
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Henrion, Didier. "Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems." Kybernetika 48.6 (2012): 1089-1099. <http://eudml.org/doc/251400>.

@article{Henrion2012,
abstract = {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.},
author = {Henrion, Didier},
journal = {Kybernetika},
keywords = {dynamical systems; invariant measures; semidefinite programming; dynamical systems; invariant measures; semidefinite programming},
language = {eng},
number = {6},
pages = {1089-1099},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems},
url = {http://eudml.org/doc/251400},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Henrion, Didier
TI - Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 6
SP - 1089
EP - 1099
AB - 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.
LA - eng
KW - dynamical systems; invariant measures; semidefinite programming; dynamical systems; invariant measures; semidefinite programming
UR - http://eudml.org/doc/251400
ER -

References

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