In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous multifunction with respect to the invariant measure of an IFSP. These results are in line with some recent extensions of IFS theory to multifunctions.
A Chaos game algorithm for generalized iterated function systems / D. La Torre, F. Mendivil. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 224:(2013 Nov 01), pp. 238-249. [10.1016/j.amc.2013.08.049]
A Chaos game algorithm for generalized iterated function systems
D. La TorrePrimo
;
2013
Abstract
In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous multifunction with respect to the invariant measure of an IFSP. These results are in line with some recent extensions of IFS theory to multifunctions.
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