[{"acknowledgement":"We thank the anonymous referee for identifying an error in an earlier\r\nversion of the paper. We gratefully acknowledge support from UKRI Frontier Research\r\nGrant EP/X033813/1, ERC grant DynAMiCS (101167561) and DFG grant 389792660 as\r\npart of TRR 248. J.O. is also affiliated with Keble College, Oxford as an Emmy Network\r\nfellow.","ddc":["000"],"scopus_import":"1","month":"07","publication_status":"epub_ahead","author":[{"id":"2e0132b3-4e98-11ef-b275-cf7281c2802a","first_name":"Pavol","full_name":"Kebis, Pavol","last_name":"Kebis"},{"full_name":"LUCA, FLORIAN","last_name":"LUCA","first_name":"FLORIAN"},{"first_name":"JOEL","full_name":"OUAKNINE, JOEL","last_name":"OUAKNINE"},{"first_name":"ANDREW","last_name":"SCOONES","full_name":"SCOONES, ANDREW"},{"first_name":"JAMES","full_name":"WORRELL, JAMES","last_name":"WORRELL"}],"department":[{"_id":"ToHe"},{"_id":"GradSch"}],"page":"1-22","oa_version":"Published Version","language":[{"iso":"eng"}],"supplementarymaterial":"no","OA_place":"publisher","das_tickbox":"0","has_accepted_license":"1","OA_type":"hybrid","citation":{"ieee":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, and J. WORRELL, “Transcendence for Pisot morphic words over an algebraic base,” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, pp. 1–22, 2026.","chicago":"Kebis, Pavol, FLORIAN LUCA, JOEL OUAKNINE, ANDREW SCOONES, and JAMES WORRELL. “Transcendence for Pisot Morphic Words over an Algebraic Base.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/etds.2026.10324\">https://doi.org/10.1017/etds.2026.10324</a>.","mla":"Kebis, Pavol, et al. “Transcendence for Pisot Morphic Words over an Algebraic Base.” <i>Ergodic Theory and Dynamical Systems</i>, Cambridge University Press, 2026, pp. 1–22, doi:<a href=\"https://doi.org/10.1017/etds.2026.10324\">10.1017/etds.2026.10324</a>.","ista":"Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. 2026. Transcendence for Pisot morphic words over an algebraic base. Ergodic Theory and Dynamical Systems., 1–22.","ama":"Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. Transcendence for Pisot morphic words over an algebraic base. <i>Ergodic Theory and Dynamical Systems</i>. 2026:1-22. doi:<a href=\"https://doi.org/10.1017/etds.2026.10324\">10.1017/etds.2026.10324</a>","apa":"Kebis, P., LUCA, F., OUAKNINE, J., SCOONES, A., &#38; WORRELL, J. (2026). Transcendence for Pisot morphic words over an algebraic base. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2026.10324\">https://doi.org/10.1017/etds.2026.10324</a>","short":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and Dynamical Systems (2026) 1–22."},"article_processing_charge":"Yes (in subscription journal)","day":"10","publication":"Ergodic Theory and Dynamical Systems","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-07-10T00:00:00Z","_id":"22406","external_id":{"arxiv":["2405.05279"]},"date_created":"2026-07-27T05:53:25Z","year":"2026","keyword":["balanced-pair algorithm","Cobham’s conjecture","k-Bonacci words","Pisot conjecture","subspace theorem"],"status":"public","doi":"10.1017/etds.2026.10324","date_updated":"2026-08-03T06:17:50Z","arxiv":1,"mathsc":["11J81","37B10","11J87"],"oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"researchdata_availability":"no","publisher":"Cambridge University Press","PlanS_conform":"1","title":"Transcendence for Pisot morphic words over an algebraic base","quality_controlled":"1","abstract":[{"text":"It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞\r\n𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞\r\n𝑛=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.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/etds.2026.10324"}],"publication_identifier":{"eissn":["1469-4417"],"issn":["0143-3857"]}},{"date_published":"2025-02-01T00:00:00Z","external_id":{"isi":["001308182000001"]},"_id":"18112","date_created":"2024-09-22T22:01:43Z","file_date_updated":"2025-01-13T08:51:40Z","year":"2025","article_processing_charge":"Yes (via OA deal)","day":"01","publication":"Ergodic Theory and Dynamical Systems","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","file":[{"date_updated":"2025-01-13T08:51:40Z","success":1,"file_id":"18828","checksum":"650fe115d998fe0ac3a8d0c7519447c8","content_type":"application/pdf","date_created":"2025-01-13T08:51:40Z","relation":"main_file","creator":"dernst","file_size":659100,"access_level":"open_access","file_name":"2025_ErgodicTheory_Henheik.pdf"}],"publisher":"Cambridge University Press","quality_controlled":"1","abstract":[{"lang":"eng","text":"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."}],"title":"Deformational rigidity of integrable metrics on the torus","publication_identifier":{"issn":["0143-3857"],"eissn":["1469-4417"]},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","call_identifier":"H2020"}],"date_updated":"2026-07-29T13:18:16Z","status":"public","doi":"10.1017/etds.2024.48","oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"page":"467-503","oa_version":"Published Version","language":[{"iso":"eng"}],"acknowledgement":"I am very grateful to Vadim Kaloshin for suggesting the topic, his guidance during this project, and many helpful comments on an earlier version of the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr Riabov for interesting discussions. Partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received funding from the European Research Council (ERC) ERC Grant No. 885707.","intvolume":"        45","ddc":["510"],"scopus_import":"1","volume":45,"month":"02","publication_status":"published","isi":1,"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"}],"department":[{"_id":"LaEr"}],"ec_funded":1,"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"has_accepted_license":"1","OA_type":"hybrid","issue":"2","corr_author":"1","citation":{"ama":"Henheik SJ. Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. 2025;45(2):467-503. doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>","apa":"Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>","short":"S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.","ieee":"S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025.","chicago":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>.","mla":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>.","ista":"Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503."},"OA_place":"publisher"}]