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1
Content available remote Markov operators acting on Polish spaces
100%
Szarek T.
Annales Polonici Mathematici
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1997
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tom 67
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nr 3
247-257
EN
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
2
Content available remote Generic properties of learning systems
100%
Szarek T.
Annales Polonici Mathematici
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2000
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tom 73
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nr 2
93-103
EN
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
3
Content available remote Generic properties of continuous iterated function systems with place dependent probabilities
80%
Bielaczyc T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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tom Vol. 55, no 1
81-96
EN
It is shown that for a typical continuous learning system denned on a compact convex subset of R[sup]n the Hausdorff dimension of its invariant measure is equal to zero.
4
Content available remote Markov operators on the space of vector measures; coloured fractals
70%
Baron K. , Lasota A.
Annales Polonici Mathematici
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1998
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tom 69
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nr 3
217-234
EN
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
5
Content available remote Infinite Graph-Directed Systems and Hausdorff Dimension
70%
Priyadarshi A.
Waves, Wavelets and Fractals
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2017
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tom 3
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nr 1
84-95
EN
In this paper we study infinite graph-directed iterated function systems on compact metric spaces given by contractive ‘infinitesimal similitudes’. We derive formula for the Hausdorff dimension of the ‘invariant set’ for such a system in terms of the spectral radii of the naturally associated family of the ‘Perron- Frobenius operators’. The results in this paper generalizes the results obtained in [20], where finite graphdirected systems and infinite iterated function systems are considered
6
Content available remote An application of the Kantorovich-Rubinstein maximum principle in the stability theory of Markov operators
60%
Gacki H.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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tom Vol. 46, no 2
215--223
EN
We consider the asymptotic behaviour of Markov operators acting on measures, defined on a locally are [sigma]-compact metric space. We prove a new sufficient condition for the asymptotic stability of Markov operators. This condition is applied to stochastically peturbed dynamical systems, and iterated function system.
7
Content available remote Generic properties of continuous iterated function systems
60%
Szarek T.
Bulletin of the Polish Academy of Sciences. Mathematics
|
1999
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tom Vol. 47, no 1
77--89
EN
It is shown that in the space of all nonexpansive continuous IFS's defined on a compact convex subset of R^n the family of asymptotically stable IFS's having a singular stationary distribution is generic.
8
Content available remote Iterated function systems generated by strict contractions and place-dependent probabilities
51%
Zaharopol R.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2000
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tom Vol. 48, no 4
429--438
EN
Let (w[sub l], w[sub 2],...,w[sub k];p[sub 1],p[sub 2],...p[sub k]) be an iterated function system (IFS for short) with continuous place-dependent probabilities, defined on a metric space (X, d). Assume that every closed ball in X is compact. Our main result is that the IFS has an attractive probability measure whenever the following three conditions are satisfied: (1) w[sub i] : X --> X is a strict contraction for every i = 1,...,k. (2) sum[...]p[sub i](x)p[sub i](y) > 0 for every x, y [belongs to] X. (3) There exists p > 0 in R such that [...] for every x, y [belongs to] X and j = l, 2,...,k. Note that we do not require the p[sub i]'s to be even uniformly continuous. This research was motivated by a question of Barnsley, Demko, Elton, and Geronimo, [1, p. 373], concerning IFS which satisfy only condition (1). We construct a family C of IFS which we use to answer the question. Our main result allows us to distinguish IFS in C which possess attractive probabilities.
9
Content available remote On a dimension of measures
41%
Lasota A. , Myjak J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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tom Vol. 50, no 2
221-235
EN
Using the notion of the Levy concentration function we discuss a definition of the dimension for probability measures. This dimension is strongly connected with the correlation dimension of measures and with the Hausdorff dimension of sets. Moreover, we calculate some bounds of this dimension for measures generated by Iterated Function Systems and by a partial differential equation.
10
Content available remote Semifractals on Polish spaces
41%
Lasota A. , Myjak J.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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tom Vol. 46, no 2
179--196
EN
We extend the theory of semifractals to arbitrary metric spaces. We also show kow to construct semifractals on Polish spaces by a use of Markov operators and Markov chain.
11
Image representation and generation by ifs and Petri nets
41%
Lumini A.
Image Processing & Communications
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2000
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tom Vol. 6, no 3-4
3-11
EN
Image generation has been proposed for many different tasks in the literature, from physics events visualization to large databases creation, from creative design to the purpose of "art for art's sake". In this paper a new approach to computer image generation is presented: the method creates new images by randomizing the decompression process, starting from a compressed representation of an image by Iterate Function Systems. Petri Nets are employed both for modeling the decompression process and for inserting a randomization component in it. A second method proposed in this work directly translates the evolution of a Petri Net into a graphic output. Experimental results are given, showing different class of images generated by the two methods.
12
Content available remote Attractors of multifunetions
41%
Lasota A. , Myjak J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2000
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tom Vol. 48, no 3
319--334
EN
We introduce the notion of a semiattractor and attractor for multifunctions and we show that they have properties similar to semifractals and fractals. Further we show a relationship between the multifunctions and transition functions appearing in the theory of Markov operators.
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