{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:58:47Z","timestamp":1790881127381,"version":"4.1.0"},"reference-count":40,"publisher":"American Physical Society (APS)","issue":"6","license":[{"start":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T00:00:00Z","timestamp":1782432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/X027422\/1"],"award-info":[{"award-number":["EP\/X027422\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,6,10]]},"abstract":"<jats:p>We show that the statistics of chaotic systems can be predicted by constructing an associated sequence of periodic differential operators and computing their densities of states. For such operators, the density of states is well understood and can be computed straightforwardly, often yielding explicit formulas. As a case study, we investigate a nonlinear recursion relation that maps naturally onto a family of periodic operators generated by a Fibonacci tiling rule. This correspondence enables us to derive an explicit formula for the limiting statistics of the chaotic system and to demonstrate that the clustering near critical values is equivalent to the van Hove singularities in the operators' densities of states.<\/jats:p>","DOI":"10.1103\/5pjc-hwjw","type":"journal-article","created":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T19:15:18Z","timestamp":1781118918000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Van Hove singularities in the density of states of a chaotic dynamical system"],"prefix":"10.1103","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8108-2316","authenticated-orcid":true,"given":"Bryn","family":"Davies","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01a77tt86","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Warwick"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,6,26]]},"reference":[{"key":"5pjc-hwjwCc1R1","volume-title":"Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics","author":"A. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"064211"}}