Pith. sign in

REVIEW 3 cited by

Interval Translation Maps with Weakly Mixing Attractors

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 2312.10533 v1 pith:LWS7O2YH submitted 2023-12-16 math.DS

Henk Bruin , Silvia Radinger This is my paper · ORCID
classification math.DS
keywords alphabetamixingwhethercantordecideintervalmaps
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We study linear recurrence and weak mixing of a two-parameter family of interval translation maps $T_{\alpha,\beta}$ for the subset of parameter space where $T_{\alpha,\beta}$ has a Cantor attractor. For this class, there is a procedure similar to the Rauzy induction which acts as a dynamical system $G$ on parameter space, which was used previously to decide whether $T_{\alpha,\beta}$ has an attracting Cantor set, and if so, whether $T_{\alpha,\beta}$ is uniquely ergodic. In this paper we use properties of $G$ to decide whether $T_{\alpha,\beta}$ is linearly recurrent or weak mixing.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Density of Stable Interval Translation Maps

    math.DS 2024-11 conditional novelty 8.0 of 10

    For interval translation maps on any fixed number of intervals, the stable, finite-type maps form an open and dense subset of parameter space.

  2. Continuous eigenvalues of minimal subshifts via S-adic representations and coboundaries

    math.DS 2026-02 conditional novelty 7.0 of 10

    Continuous eigenvalues of minimal subshifts are characterized by letter-coboundaries along recognizable, decisive S-adic structures.

  3. Renormalization for Bruin-Troubetzkoy ITMs

    math.DS 2024-12 conditional novelty 7.0 of 10

    The ARC renormalization yields a natural measure on infinite-type Bruin-Troubetzkoy interval translations, proves unique ergodicity almost everywhere, bounds the Hausdorff dimension of the parameter set between 1.5 an...

Pith tools