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- W2342969148 abstract "In 1987, J. H. Elton, has proved the first fundamental result in convergence of IFS, the Elton's Ergodic Theorem. In this work we prove the natural extension of this theorem to the projected Hutchinson measure $mu_{alpha}$ associated to a GIFSpdp $mathcal{S}=left(X, (phi_j:X^{m} to X)_{j=0,1, ..., n-1}, (p_j)_{j=0,1, ..., n-1}right),$ in a compact metric space $(X,d)$. More precisely, the average along of the trajectories $x_{n}(a)$ of the GIFS, starting in any initial points $x_0, ..., x_{m-1} in X$ satisfies, for any $f in C(X , mathbb{R})$, $$lim_{Nto +infty} frac{1}{N}sum_{n=0 }^{N-1} f(x_{n}(a)) = int_{X} f(t) dmu_{alpha}(t),$$ for almost all $a in Omega={0,1, ..., n-1}^{mathbb{N}}$, the symbolic space. Additionally, we give some examples and applications to Chaos Games and Nonautonomous Dynamical Systems defined by finite difference equations." @default.
- W2342969148 created "2016-06-24" @default.
- W2342969148 creator A5054897857 @default.
- W2342969148 date "2015-07-18" @default.
- W2342969148 modified "2023-09-27" @default.
- W2342969148 title "The Ergodic Theorem for a new kind of attractor of a GIFS" @default.
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