Countably piecewise expanding transformations without absolutely continuous invariant measure
On small stochastic perturbations of mappings of the unit interval
Ruch drogowy a sztuczna inteligencja
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Invariant measures and the compactness of the domain
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 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.
Position dependent random maps in one and higher dimensions
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.
A comparative dynamical analysis of Hebrew texts.
Invariant measures for Chebyshev maps.
A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.
Invariant densities of random maps have lower bounds on their supports.
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