Regular potentials of additive functionals in semidynamical systems

Nedra Belhaj Rhouma; Mounir Bezzarga

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 555-572
  • ISSN: 0010-2628

Abstract

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We consider a semidynamical system ( X , ℬ , Φ , w ) . We introduce the cone 𝔸 of continuous additive functionals defined on X and the cone 𝒫 of regular potentials. We define an order relation “ ≤ ” on 𝔸 and a specific order “ ≺ ” on 𝒫 . We will investigate the properties of 𝔸 and 𝒫 and we will establish the relationship between the two cones.

How to cite

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Rhouma, Nedra Belhaj, and Bezzarga, Mounir. "Regular potentials of additive functionals in semidynamical systems." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 555-572. <http://eudml.org/doc/249342>.

@article{Rhouma2004,
abstract = {We consider a semidynamical system $(X,\mathcal \{B\},\Phi ,w)$. We introduce the cone $\mathbb \{A\}$ of continuous additive functionals defined on $X$ and the cone $\mathcal \{P\}$ of regular potentials. We define an order relation “$\le $” on $\mathbb \{A\}$ and a specific order “$\prec $” on $\mathcal \{P\}$. We will investigate the properties of $\mathbb \{A\}$ and $\mathcal \{P\}$ and we will establish the relationship between the two cones.},
author = {Rhouma, Nedra Belhaj, Bezzarga, Mounir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {additive functional; excessive functions; regular potential; semidynamical system; specific order; additive functional; excessive functions; regular potential; semidynamical system; specific order},
language = {eng},
number = {3},
pages = {555-572},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Regular potentials of additive functionals in semidynamical systems},
url = {http://eudml.org/doc/249342},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Rhouma, Nedra Belhaj
AU - Bezzarga, Mounir
TI - Regular potentials of additive functionals in semidynamical systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 555
EP - 572
AB - We consider a semidynamical system $(X,\mathcal {B},\Phi ,w)$. We introduce the cone $\mathbb {A}$ of continuous additive functionals defined on $X$ and the cone $\mathcal {P}$ of regular potentials. We define an order relation “$\le $” on $\mathbb {A}$ and a specific order “$\prec $” on $\mathcal {P}$. We will investigate the properties of $\mathbb {A}$ and $\mathcal {P}$ and we will establish the relationship between the two cones.
LA - eng
KW - additive functional; excessive functions; regular potential; semidynamical system; specific order; additive functional; excessive functions; regular potential; semidynamical system; specific order
UR - http://eudml.org/doc/249342
ER -

References

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  9. Boboc N., Bucur Gh., Potential theory on ordered sets II, Rev. Roumaine Math. Pures Appl. 43 (1998), 685-720. (1998) Zbl0995.31008MR1845086
  10. Dellacherie C., Meyer P.A., Probabilités et potentiel, Chap. XV, Hermann, Paris, 1987. Zbl0624.60084MR0488194
  11. Getoor R.K., Transience and Recurrence of Markov Process, Séminaire de Probabilité XIV 1978-1979, Lecture Notes in Math. 784, Springer, Berlin, 1980, pp.397-409. MR0580144
  12. Hájek O., Dynamical Systems in the Plane, Academic Press, London-New York, 1968. MR0240418
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  14. Sharpe M., General Theory of Markov Process, Pure and Applied Mathematics, 133, Academic Press, Inc., Boston, MA, 1988. MR0958914

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