Matches in SemOpenAlex for { <https://semopenalex.org/work/W2964073301> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2964073301 endingPage "817" @default.
- W2964073301 startingPage "773" @default.
- W2964073301 abstract "Abstract Let $K$ be a finitely generated field of characteristic zero. For fixed $mgeqslant 2$ , we study the rational functions $unicode[STIX]{x1D719}$ defined over $K$ that have a $K$ -orbit containing infinitely many distinct $m$ -th powers. For $mgeqslant 5$ we show that the only such functions are those of the form $cx^{j}(unicode[STIX]{x1D713}(x))^{m}$ with $unicode[STIX]{x1D713}in K(x)$ , and for $mleqslant 4$ we show that the only additional cases are certain Lattès maps and four families of rational functions whose special properties appear not to have been studied before. With additional analysis, we show that the index set ${ngeqslant 0:unicode[STIX]{x1D719}^{n}(a)in unicode[STIX]{x1D706}(mathbb{P}^{1}(K))}$ is a union of finitely many arithmetic progressions, where $unicode[STIX]{x1D719}^{n}$ denotes the $n$ -th iterate of $unicode[STIX]{x1D719}$ and $unicode[STIX]{x1D706}in K(x)$ is any map Möbius-conjugate over $K$ to $x^{m}$ . When the index set is infinite, we give bounds on the number and moduli of the arithmetic progressions involved. These results are similar in flavor to the dynamical Mordell–Lang conjecture, and motivate a new conjecture on the intersection of an orbit with the value set of a morphism. A key ingredient in our proofs is a study of the curves $y^{m}=unicode[STIX]{x1D719}^{n}(x)$ . We describe all $unicode[STIX]{x1D719}$ for which these curves have an irreducible component of genus at most 1, and show that such $unicode[STIX]{x1D719}$ must have two distinct iterates that are equal in $K(x)^{ast }/K(x)^{ast m}$ ." @default.
- W2964073301 created "2019-07-30" @default.
- W2964073301 creator A5001570714 @default.
- W2964073301 creator A5034614653 @default.
- W2964073301 creator A5070782362 @default.
- W2964073301 date "2019-01-09" @default.
- W2964073301 modified "2023-10-18" @default.
- W2964073301 title "Powers in Orbits of Rational Functions: Cases of an Arithmetic Dynamical Mordell–Lang Conjecture" @default.
- W2964073301 cites W1556269828 @default.
- W2964073301 cites W1557415002 @default.
- W2964073301 cites W1558611215 @default.
- W2964073301 cites W1562839392 @default.
- W2964073301 cites W1591377231 @default.
- W2964073301 cites W1908064275 @default.
- W2964073301 cites W1977816843 @default.
- W2964073301 cites W2072386919 @default.
- W2964073301 cites W2075641017 @default.
- W2964073301 cites W2087041722 @default.
- W2964073301 cites W2105937858 @default.
- W2964073301 cites W2163155542 @default.
- W2964073301 cites W2315220517 @default.
- W2964073301 cites W2486137719 @default.
- W2964073301 cites W2949477212 @default.
- W2964073301 cites W3099251544 @default.
- W2964073301 cites W3103163627 @default.
- W2964073301 cites W315047097 @default.
- W2964073301 cites W4229633778 @default.
- W2964073301 cites W4244515083 @default.
- W2964073301 cites W600543299 @default.
- W2964073301 doi "https://doi.org/10.4153/cjm-2018-026-x" @default.
- W2964073301 hasPublicationYear "2019" @default.
- W2964073301 type Work @default.
- W2964073301 sameAs 2964073301 @default.
- W2964073301 citedByCount "4" @default.
- W2964073301 countsByYear W29640733012019 @default.
- W2964073301 countsByYear W29640733012021 @default.
- W2964073301 countsByYear W29640733012022 @default.
- W2964073301 crossrefType "journal-article" @default.
- W2964073301 hasAuthorship W2964073301A5001570714 @default.
- W2964073301 hasAuthorship W2964073301A5034614653 @default.
- W2964073301 hasAuthorship W2964073301A5070782362 @default.
- W2964073301 hasBestOaLocation W29640733011 @default.
- W2964073301 hasConcept C114614502 @default.
- W2964073301 hasConcept C118615104 @default.
- W2964073301 hasConcept C136119220 @default.
- W2964073301 hasConcept C202444582 @default.
- W2964073301 hasConcept C204321447 @default.
- W2964073301 hasConcept C2780990831 @default.
- W2964073301 hasConcept C33923547 @default.
- W2964073301 hasConcept C41008148 @default.
- W2964073301 hasConcept C500551929 @default.
- W2964073301 hasConcept C75190567 @default.
- W2964073301 hasConcept C94375191 @default.
- W2964073301 hasConceptScore W2964073301C114614502 @default.
- W2964073301 hasConceptScore W2964073301C118615104 @default.
- W2964073301 hasConceptScore W2964073301C136119220 @default.
- W2964073301 hasConceptScore W2964073301C202444582 @default.
- W2964073301 hasConceptScore W2964073301C204321447 @default.
- W2964073301 hasConceptScore W2964073301C2780990831 @default.
- W2964073301 hasConceptScore W2964073301C33923547 @default.
- W2964073301 hasConceptScore W2964073301C41008148 @default.
- W2964073301 hasConceptScore W2964073301C500551929 @default.
- W2964073301 hasConceptScore W2964073301C75190567 @default.
- W2964073301 hasConceptScore W2964073301C94375191 @default.
- W2964073301 hasIssue "4" @default.
- W2964073301 hasLocation W29640733011 @default.
- W2964073301 hasLocation W29640733012 @default.
- W2964073301 hasOpenAccess W2964073301 @default.
- W2964073301 hasPrimaryLocation W29640733011 @default.
- W2964073301 hasRelatedWork W2029981401 @default.
- W2964073301 hasRelatedWork W2606009334 @default.
- W2964073301 hasRelatedWork W2740334431 @default.
- W2964073301 hasRelatedWork W2897153210 @default.
- W2964073301 hasRelatedWork W2963673615 @default.
- W2964073301 hasRelatedWork W2964292522 @default.
- W2964073301 hasRelatedWork W3026358768 @default.
- W2964073301 hasRelatedWork W4212808623 @default.
- W2964073301 hasRelatedWork W4309653601 @default.
- W2964073301 hasRelatedWork W4375947704 @default.
- W2964073301 hasVolume "71" @default.
- W2964073301 isParatext "false" @default.
- W2964073301 isRetracted "false" @default.
- W2964073301 magId "2964073301" @default.
- W2964073301 workType "article" @default.