{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:37:29Z","timestamp":1740141449876,"version":"3.37.3"},"reference-count":17,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,8,22]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n               <jats:p>We consider the subgroup of points of finite orbit through the action of an endomorphism of a finitely generated virtually free group, with particular emphasis on the subgroup of eventually fixed points, $\\text{EvFix}(\\varphi)$: points whose orbit contains a fixed point. We provide an algorithm to compute the subgroup of fixed points of an endomorphism of a finitely generated virtually free group and prove that finite orbits have cardinality bounded by a computable constant, which allows us to solve several algorithmic problems: deciding if \u03c6 is a finite order element of $\\text{End}(G)$, if \u03c6 is aperiodic, if $\\text{EvFix}(\\varphi)$ is finitely generated and if $\\text{EvFix}(\\varphi)$ is a normal subgroup. In the cases where $\\text{EvFix}(\\varphi)$ is finitely generated, we also present a bound for its rank and an algorithm to compute a generating set.<\/jats:p>","DOI":"10.1093\/qmath\/haae032","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T16:08:59Z","timestamp":1718208539000},"page":"851-867","source":"Crossref","is-referenced-by-count":1,"title":["Eventually fixed points of endomorphisms of virtually free groups"],"prefix":"10.1093","volume":"75","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1585-9443","authenticated-orcid":false,"given":"Andr\u00e9","family":"Carvalho","sequence":"first","affiliation":[{"name":"Centre of Mathematics, Faculty of Sciences of the University of Porto , R. 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