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We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C 3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family… (More)

We consider the equation ˙ x(t) = f (t, x(t), x(η(t))) with a variable time shift η(t). Both the nonlinearity f and the shift function η are given, and are assumed to be analytic (that is, holomorphic) functions of their arguments. Typically the time shift represents a delay, namely, that η(t) = t − r(t) with r(t) ≥ 0. The main problem considered is to… (More)

Maps / defined on the interior of the standard non-negative cone K in R. N which are both homogeneous of degree 1 and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson's part metric and continuous on the interior of the cone. It follows from more general results presented here… (More)

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