Dimension theory for linear solenoids
J\"org Neunh\"auserer
TL;DR
This paper develops the dimension theory for linear solenoids with fractal attractors, providing formulas for attractor and measure dimensions and exploring the existence of measures with full dimension.
Contribution
It introduces new formulas for the dimensions of attractors and ergodic measures in linear solenoids, advancing understanding of their fractal structure.
Findings
Derived formulas for the dimension of the attractor
Established formulas for the dimension of ergodic measures
Discussed the existence of measures of full dimension
Abstract
We develop the dimension theory for a class of linear solenoids, which have a "fractal" attractor. We will find the dimension of the attractor, proof formulas for the dimension of ergodic measures on this attractor and discuss the question whether there exists a measure of full dimension.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Theories and Applications · Cellular Automata and Applications