Estimating Hausdorff measure for Denjoy maps
{\L}ukasz Pawelec, Mariusz Urba\'nski
TL;DR
This paper develops a recurrence-based method to effectively estimate the Hausdorff measure of minimal sets in circle homeomorphisms that are not conjugate to rotations, advancing understanding of their geometric properties.
Contribution
It introduces a new recurrence method for estimating Hausdorff measures of minimal sets in non-rotation conjugate circle homeomorphisms.
Findings
Provides effective lower bounds for Hausdorff measures
Applies recurrence method to minimal sets of circle homeomorphisms
Enhances understanding of geometric complexity of non-rotation minimal sets
Abstract
By employing the recurrence method worked out in `Estimating the Hausdorff measure by recurrence', we provide effective lower estimates of the proper--dimensional Hausdorff measure of minimal sets of circle homeomorphisms that are not conjugate to any rotation.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Topological and Geometric Data Analysis