@article{22406,
  abstract     = {It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞
𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞
𝑛=0(𝑢𝑛/𝛽𝑛) either lies in ℚ⁡(𝛽) or is transcendental. In this paper, we show a similar rational–transcendental dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets. Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete spectrum), we generalise the latter result to arbitrary finite alphabets. In certain cases, we are able to show transcendence of [[𝒖]]𝛽 outright. In particular, for 𝑘 ≥2, if 𝒖 is the k-Bonacci word, then [[𝒖]]𝛽 is transcendental.},
  author       = {Kebis, Pavol and LUCA, FLORIAN and OUAKNINE, JOEL and SCOONES, ANDREW and WORRELL, JAMES},
  issn         = {1469-4417},
  journal      = {Ergodic Theory and Dynamical Systems},
  keywords     = {balanced-pair algorithm, Cobham’s conjecture, k-Bonacci words, Pisot conjecture, subspace theorem},
  pages        = {1--22},
  publisher    = {Cambridge University Press},
  title        = {{Transcendence for Pisot morphic words over an algebraic base}},
  doi          = {10.1017/etds.2026.10324},
  year         = {2026},
}

@article{18112,
  abstract     = {It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.},
  author       = {Henheik, Sven Joscha},
  issn         = {1469-4417},
  journal      = {Ergodic Theory and Dynamical Systems},
  number       = {2},
  pages        = {467--503},
  publisher    = {Cambridge University Press},
  title        = {{Deformational rigidity of integrable metrics on the torus}},
  doi          = {10.1017/etds.2024.48},
  volume       = {45},
  year         = {2025},
}