ISSN:
1432-0940
Keywords:
28D99
;
41A99
;
58F11
;
60F05
;
60G10
;
60J05
;
Iterated function systems
;
Attractor
;
Random maps
;
Markov chain
;
Ergodic
;
Lyapunov exponent
;
Fractal
;
Dimension
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Recurrent iterated function systems generalize iterated function systems as introduced by Barnsley and Demko [BD] in that a Markov chain (typically with some zeros in the transition probability matrix) is used to drive a system of mapsw j :K →K,j=1, 2,⋯,N, whereK is a complete metric space. It is proved that under “average contractivity,” a convergence and ergodic theorem obtains, which extends the results of Barnsley and Elton [BE]. It is also proved that a Collage Theorem is true, which generalizes the main result of Barnsleyet al. [BEHL] and which broadens the class of images which can be encoded using iterated map techniques. The theory of fractal interpolation functions [B] is extended, and the fractal dimensions for certain attractors is derived, extending the technique of Hardin and Massopust [HM]. Applications to Julia set theory and to the study of the boundary of IFS attractors are presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01889596
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