Storming the Lemer Limit: Experimental Study of Pisot and Salem Root Stability

This work presents an exhaustive protocol for numerical simulation of perturbed Pisotpolynomials. Using SageMath, the degradation of SALEM status and the transition to“crystalline turbulence” approaching the Lemer limit (≈ 1.17628) were recorded. Completeempirical data for bases of various orders are provided.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-01
DOI
https://doi.org/10.5281/zenodo.19346558
Primary Topic
Fluid Dynamics and Turbulent Flows
Type
article
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article

Storming the Lemer Limit: Experimental Study of Pisot and Salem Root Stability

Emma Helmdach
Zenodo (CERN European Organization for Nuclear Research)
Fluid Dynamics and Turbulent Flows
article

Storming the Lemer Limit: Experimental Study of Pisot and Salem Root Stability

Emma Helmdach
article en

Abstract

This work presents an exhaustive protocol for numerical simulation of perturbed Pisotpolynomials. Using SageMath, the degradation of SALEM status and the transition to“crystalline turbulence” approaching the Lemer limit (≈ 1.17628) were recorded. Completeempirical data for bases of various orders are provided.

Zenodo (CERN European Organization for Nuclear Research)
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Storming the Lemer Limit: Experimental Study of Pisot and Salem Root Stability — Emma Helmdach · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS