Regular Article
A Random Fixed Point Theorem and the Random Graph Transformation

https://doi.org/10.1006/jmaa.1998.6008Get rights and content
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Abstract

In the first part of this article we formulate a random fixed point theorem for random dynamical systems where a contraction condition is formulated as an expectation of a particular expression. In the following we are going to formulate a random graph transformation. This transformation defines a random dynamical system. Under certain conditions this random dynamical system has a random fixed point which can be found by the mentioned random fixed point theorem. In one application we show that random dynamical systems given by particular differential equations have a random unstable invariant manifold.

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Submitted by Jack, K. Hale

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E-mail address:[email protected].