Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1054.37014
Tricot, Claude; Riedi, Rudolf
Attractors, orbits and ergodicity. (Attracteurs, orbites et ergodicité.) (French)
[J] Ann. Math. Blaise Pascal 6, No. 1, 55-72 (1999). ISSN 1259-1734

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.\par We give a simple proof of this known result.

MSC 2000:: *37D45 Strange attractors, chaotic dynamics
28D05 Measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37B10 Symbolic dynamics
37C45 Dimension theory of dynamical systems
28A80 Fractals

Keywords: iterated function system; invariant measure; attractor; ergodic theorem; fractals; orbits; Cantor sets

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]