PreprintCC BY 4.0arXiv
Partial rigidity and q-additive functions
Abstract
A system $(X,μ, T)$ is partially rigid with constant δ>0 if there exists an incresing sequence (nk) such that liminfk → ∞ μ(A ∩ T−nkA) ≥ δμ(A) for every measurable A ⊂ X. The partial rigidity rate is the largest constant of partial rigidity. We characterize the partial rigidity rate of subshifts arising from q-additive functions pmod M in terms of quantities arising from Bésineau's theorem. With this, we build a family of strongly q-additive functions to deduce that the collection of partial rigidity rates for substitution subshifts is dense in [0,1] answering a question of Donoso, Maass and the author.
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BibTeX
@misc{radic2026partial,
title = {{Partial rigidity and q-additive functions}},
author = {Tristán Radić},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32445},
eprint = {2610.32445},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32445},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Partial rigidity and q-additive functions
AU - Tristán Radić
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32445
UR - https://arxiv.org/abs/2610.32445
AB - A system $(X,μ, T)$ is partially rigid with constant δ>0 if there exists an incresing sequence (n_k) such that liminf_k → ∞ μ(A ∩ T^−n_kA) ≥ δμ(A) for every measurable A ⊂ X. The partial rigidity rate is the largest constant of partial rigidity. We characterize the partial rigidity rate of subshifts arising from q-additive functions pmod M in terms of quantities arising from Bésineau's theorem. With this, we build a family of strongly q-additive functions to deduce that the collection of partial rigidity rates for substitution subshifts is dense in [0,1] answering a question of Donoso, Maass and the author.
ER -