Random entropy and recurrence.
Dajani, Karma, Meester, Ronald (2003)
International Journal of Mathematics and Mathematical Sciences
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Dajani, Karma, Meester, Ronald (2003)
International Journal of Mathematics and Mathematical Sciences
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Aya Hmissi, Farida Hmissi, Mohamed Hmissi (2012)
ESAIM: Proceedings
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This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic...
Wael Bahsoun, Paweł Góra (2005)
Studia Mathematica
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A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of ℝⁿ. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of ℝⁿ are the main results.
Dinis D. Pestana, Sandra M. Aleixo, J. Leonel Rocha (2009)
Discussiones Mathematicae Probability and Statistics
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Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal...
Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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Tomoki Inoue (2012)
Studia Mathematica
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We consider a family of transformations with a random parameter and study a random dynamical system in which one transformation is randomly selected from the family and applied on each iteration. The parameter space may be of cardinality continuum. Further, the selection of the transformation need not be independent of the position in the state space. We show the existence of absolutely continuous invariant measures for random maps on an interval under some conditions.
Kifer, Yuri (1998)
Documenta Mathematica
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Góra, Paweł, Boyarsky, Abraham, Islam, Md.Shafiqul (2006)
Journal of Applied Mathematics and Stochastic Analysis
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V. Gundlach, G. Ochs (2000)
Colloquium Mathematicae
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We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.
Joseph Rosenblatt (1981)
Mathematische Annalen
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R. Kaufman (1970)
Studia Mathematica
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Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)
Lobachevskii Journal of Mathematics
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Dan Voiculescu (1991)
Inventiones mathematicae
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