Invariant densities for random maps of the interval

DOI PDF PDF 被引用文献6件

この論文をさがす

説明

<p>A <italic>random map</italic> is a discrete time process in which one of a number of functions is selected at random and applied. Here we study random maps of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket 0 comma 1 right-bracket"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">[0,1]</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which represent dynamical systems on the square <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket 0 comma 1 right-bracket times left-bracket 0 comma 1 right-bracket"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">]</mml:mo> <mml:mo>×<!-- × --></mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">[0,1] \times [0,1]</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Sufficient conditions for a random map to have an absolutely continuous <italic>invariant measure</italic> are given, and the number of <italic>ergodic components</italic> of a random map is discussed.</p>

収録刊行物

被引用文献 (6)*注記

もっと見る

問題の指摘

ページトップへ