Ergodic properties of Markov maps inR
d |
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Authors: | Piotr Bugiel |
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Institution: | (1) Department of Mathematics, Jagellonian University, ul. Reymonta 4, PL-30-059 Kraków, Poland |
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Abstract: | Summary For domainsI R
d
(bounded or not) the notion of a Markov map fromI into itself is developed. It is shown that under a condition of Rényi type and the assumption that the map is Markov, any probability density tends inL
1-norm to a unique invariant measure under the action of the Perron-Frobenius operatorP
. The smoothness and ergodic properties of that invariant measure are studied. The paper generalizes results of Lasota and Yorke from dimension one to higher dimension. |
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Keywords: | |
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