On a Continuous Sárközy-Type Problem

Autor: Borys Kuca, Tuomas Orponen, Tuomas Sahlsten

Publikováno v: International Mathematics Research Notices.

We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45a9ac2aad7d294b8361a0383de4f1e4
https://doi.org/10.1093/imrn/rnac168

Entropy in uniformly quasiregular dynamics

Autor: Ilmari Kangasniemi, Yûsuke Okuyama, Tuomas Sahlsten, Pekka Pankka

Let $M$ be a closed, oriented, and connected Riemannian $n$-manifold, for $n\ge 2$, which is not a rational homology sphere. We show that, for a non-constant and non-injective uniformly quasiregular self-map $f\colon M\to M$, the topological entropy

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8976130ab6a9aa9dcdae0da8d7a92732

Stability and perturbations of countable Markov maps

Autor: Tuomas Sahlsten, Sara Munday, Thomas Jordan

Publikováno v: Jordan, T, Munday, S & Sahlsten, T 2018, ' Stability and perturbations of countable Markov maps ', Nonlinearity, vol. 31, no. 4, pp. 1351-1377 . https://doi.org/10.1088/1361-6544/aa9d5b

Let T and Tϵ, ϵ > 0, be countable Markov maps such that the branches of Tϵ converge pointwise to the branches of T, as ϵ → 0. We study the stability of various quantities measuring the singularity (dimension, Hölder exponent etc) of the topolo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d47298b9dfe640366422cc0749be2298
https://research-information.bris.ac.uk/ws/files/137369908/perturbationsMarkov.pdf

Intermediate $\beta$-shifts of finite type

Autor: Tony Samuel, Bing Li, Tuomas Sahlsten

Publikováno v: Li, B, Sahlsten, T & Samuel, T 2016, ' Intermediate beta-shifts of finite type ', Discrete and Continuous Dynamical Systems, vol. 36, no. 1, pp. 323-344 . https://doi.org/10.3934/dcds.2016.36.323

An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, $\beta$-shift (transformation) and an intermediate $\beta$-shift (transformation), for a fixed $\beta \in (1, 2)$. Specifically, a classification in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95e0907e6a5269990b8f55964b374882
https://doi.org/10.3934/dcds.2016.36.323

Quantum ergodicity and Benjamini–Schramm convergence of hyperbolic surfaces

Autor: Tuomas Sahlsten, Etienne Le Masson

Publikováno v: Duke Math. J. 166, no. 18 (2017), 3425-3460
Duke Mathematical Journal
Le Masson, E & Sahlsten, T 2017, ' Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces ', Duke Mathematical Journal, vol. 166, no. 18, pp. 3425-3460 . https://doi.org/10.1215/00127094-2017-0027
Sahlsten, T & Le Masson, E 2017, ' Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces ', Duke Mathematical Journal, vol. 166, no. 18, pp. 3425-3460 . https://doi.org/10.1215/00127094-2017-0027

We present a quantum ergodicity theorem for fixed spectral window and sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini and Schramm. This addresses a question posed by Colin de Verdi\`{e}re. Our the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66600c817bc29fa0487419466f855ec9
https://doi.org/10.1215/00127094-2017-0027