Attractors, orbits and ergodicity. (Attracteurs, orbites et ergodicité.) (French) Zbl 1054.37014

Summary: The attractor of a system of iterated functions is the support of a measure called invariant or auto-similar: it is the fixed point of the Markov operator in the metric space of probability measures with compact support. A random algorithm permits the construction of the attractor which is almost sure the limit points set of an orbit. With the help of an ergodic theorem one can prove that the visit frequency of a set through this orbit is almost sure equal to the invariant measure of this set.
We give a simple proof of this known result.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
28D05 Measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37B10 Symbolic dynamics
37C45 Dimension theory of smooth dynamical systems
28A80 Fractals
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