6533b859fe1ef96bd12b6ef5
RESEARCH PRODUCT
Local structure of self-affine sets
Antti KäenmäkiChristoph Bandtsubject
Pure mathematicsMathematics::Dynamical SystemsApplied MathematicsGeneral Mathematicsta111Open setStructure (category theory)MagnificationDynamical Systems (math.DS)Local structureSet (abstract data type)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 37D45Mathematicsdescription
The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self-affine Cantor sets E of the type studied by Bedford, McMullen, Gatzouras and Lalley, for which the projection onto the horizontal axis is an interval. We show that within small square neighborhoods of almost each point x in E, with respect to many product measures on address space, E is well approximated by product sets of an interval and a Cantor set. Even though E is totally disconnected, the limit sets have the product structure with interval fibres, reminiscent to the view of attractors of chaotic differentiable dynamical systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-04-01 | Ergodic Theory and Dynamical Systems |