Pith. sign in

REVIEW 1 cited by

Path-dependent shrinking targets in generic affine iterated function systems

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2210.05362 v1 pith:XWQ6OCLB submitted 2022-10-11 math.DS math.CA

Henna Koivusalo , Lingmin Liao , Michal Rams This is my paper · ORCID
classification math.DSmath.CA
keywords functiongenericpath-dependentshrinkingaffinedimensionhausdorffiterated
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We calculate the Hausdorff dimension of path-dependent shrinking target sets in generic affine iterated function systems. Here, by a path-dependent shrinking target set, we mean a set of points whose orbits infinitely often hit small balls with a fixed generic centre and with radius decreasing and dependent on the point itself. It turns out that the Hausdorff dimension of such a set is given by the zero point of a certain limsup pressure function. The result generalizes the work of Koivusalo and Ramirez, and Barany and Troscheit, as well as that of Hill and Velani.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dichotomy laws for the Hausdorff measure of shrinking target sets in $\beta$-dynamical systems

    math.DS 2024-11 reject novelty 7.0 of 10

    For beta-dynamical systems with integer bases, the Hausdorff f-measure of shrinking target sets is zero or full according to divergence of an explicit series.

Pith tools