On the Hausdorff dimension of a family of self-similar sets with complicated overlaps

• Autorzy: Balázs Bárány
• Języki publikacji: EN

Abstrakty

EN

We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff dimension of the attractor is strictly smaller.

Kategorie tematyczne

• 37C45: Dimension theory of dynamical systems
• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 49-59

Daty

wydano

2009

Twórcy

autor

Balázs Bárány

• Department of Stochastics, Institute of Mathematics, Technical University of Budapest, P.O. Box 91, 1521 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm206-0-4