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Countably piecewise expanding transformations without absolutely continuous invariant measure

100%

Góra P.

Banach Center Publications

|

1989

|

tom 23

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nr 1

113-117

2

Invariant measures and the compactness of the domain

72%

Jabłoński M., Góra P.

Annales Polonici Mathematici

|

1998

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tom 69

|

nr 1

13-24

EN

We consider piecewise monotonic and expanding transformations τ of a real interval (not necessarily bounded) into itself with countable number of points of discontinuity of τ' and with some conditions on the variation $V_{[0,x]}(1/|τ'|)$ which need not be a bounded function (although it is bounded on any compact interval). We prove that such transformations have absolutely continuous invariant measures. This result generalizes all previous "bounded variation" existence theorems.

3

Position dependent random maps in one and higher dimensions

72%

Bahsoun W., Góra P.

Studia Mathematica

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2005

|

tom 166

|

nr 3

271-286

EN

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.

4

On small stochastic perturbations of mappings of the unit interval

50%

Góra P.

Colloquium Mathematicum

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1984-1985

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tom 49

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nr 1

73-85

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

1 Colloquium Mathematicum

1 Studia Mathematica

4 Góra P.

1 Bahsoun W.

1 Jabłoński M.

1 2005

1 1998

1 1989

1 1984

Countably piecewise expanding transformations without absolutely continuous invariant measure

Invariant measures and the compactness of the domain

Position dependent random maps in one and higher dimensions

On small stochastic perturbations of mappings of the unit interval