Hausdorff and packing dimension of Diophantine sets
Antoine Marnat
TL;DR
This paper calculates the Hausdorff and packing dimensions of Diophantine approximation sets using variational principles, extending classical results to intermediate exponents.
Contribution
It introduces a method to compute dimensions of Diophantine sets related to exponents, extending previous results to new cases.
Findings
Dimensions of Diophantine sets are explicitly computed.
Extension of classical results to intermediate exponents.
Application of variational principles in parametric geometry of numbers.
Abstract
Using the variational principle in parametric geometry of numbers, we compute the Hausdorff and packing dimension of Diophantine sets related to exponents of Diophantine approximation, and their intersections. In particular, we extend a result of Jarn\'ik and Besicovitch to intermediate exponents.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Advanced Topology and Set Theory