The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

• Autorzy: Michael Keane , K. Károly , Boris Solomyak
• Języki publikacji: EN

Abstrakty

EN

Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.

Kategorie tematyczne

• 37C45: Dimension theory of dynamical systems
• 28A78: Hausdorff and packing measures
• 94A08: Image processing (compression, reconstruction, etc.)
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 180
• Numer: 3
• Strony: 279-292

Daty

wydano

2003

Twórcy

autor

Michael Keane

• Mathematics Department, Wesleyan University, Middletown, CT 06459, U.S.A.
• CWI, University of Amsterdam, Amsterdam, The Netherlands

autor

K. Károly

• Institute of Mathematics, Technical University of Budapest, P.O. Box 91, H-1529 Budapest, Hungary

autor

Boris Solomyak

• Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, U.S.A.

Identyfikatory

DOI

10.4064/fm180-3-5