Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5499807 | Chaos, Solitons & Fractals | 2017 | 9 Pages |
Abstract
In 1987, Elton [11], has proved the first fundamental result on the convergence of IFS, the Elton's Ergodic Theorem. In this work we prove the natural extension of this theorem to the projected Hutchinson measure μα associated to a GIFSpdp S=(X,(Ïj:XmâX)j=0,1,â¦,nâ1,(pj)j=0,1,â¦,nâ1), in a compact metric space (X, d). More precisely, the average along of the trajectories xn(a) of the GIFS, starting in any initial points x0,â¦,xmâ1âX satisfies, for any fâC(X,R),limNâ+â1Nân=0Nâ1f(xn(a))=â«Xf(t)dμα(t),for almost all aâΩ={0,1,â¦,nâ1}N, the symbolic space. Additionally, we give some examples and applications to Chaos Games and Nonautonomous Dynamical Systems defined by finite difference equations.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Elismar R. Oliveira,