{"id":"https://openalex.org/W7221754635","doi":"https://doi.org/10.48550/arxiv.2610.17650","title":"Simultaneously preperiodic points and colliding orbits for families of polynomials in characteristic $p$","display_name":"Simultaneously preperiodic points and colliding orbits for families of polynomials in characteristic $p$","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221754635","doi":"https://doi.org/10.48550/arxiv.2610.17650"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.17650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17650","pdf_url":"https://arxiv.org/pdf/2610.17650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.17650","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158715577","display_name":"Jungin Lee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Jungin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031049072","display_name":"GyeongHyeon Nam","orcid":"https://orcid.org/0000-0002-7868-7119","observed_orcids":["https://orcid.org/0000-0002-7868-7119"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nam, GyeongHyeon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8314999938011169,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8314999938011169,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.1492999941110611,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preperiodic-points","display_name":"preperiodic points","score":0.9629999995231628},{"id":"https://openalex.org/keywords/polynomial-families","display_name":"polynomial families","score":0.8799999952316284},{"id":"https://openalex.org/keywords/algebraically-closed-fields","display_name":"algebraically closed fields","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.78329998254776},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5691999793052673},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5674999952316284},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5081999897956848},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5006999969482422},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45249998569488525},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.26899999380111694}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.17650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17650","pdf_url":"https://arxiv.org/pdf/2610.17650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.17650","doi":"https://doi.org/10.48550/arxiv.2610.17650","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.17650","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.17650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17650","pdf_url":"https://arxiv.org/pdf/2610.17650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2860470529","display_name":null,"funder_award_id":"RS-2024-00334558","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G4362420071","display_name":null,"funder_award_id":"RS-2025-02262988","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5727368902","display_name":null,"funder_award_id":"RS-2024-00334558","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G7879179447","display_name":null,"funder_award_id":"RS-2025-02262988","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221754635.pdf","grobid_xml":"https://content.openalex.org/works/W7221754635.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4417077825"],"related_works":["https://openalex.org/W4417077825","https://openalex.org/W4417253932","https://openalex.org/W1993188844","https://openalex.org/W4405340450","https://openalex.org/W2055422594","https://openalex.org/W7171712732","https://openalex.org/W4415193851","https://openalex.org/W2786905345","https://openalex.org/W2539627085","https://openalex.org/W3094045558"],"abstract_inverted_index":{"Let":[0],"$k=\\overline{\\mathbb{F}}_p$":[1],"and":[2,47,73],"let":[3],"$f\\in":[4],"k[X]$":[5],"be":[6,83],"a":[7,71],"polynomial":[8],"of":[9,27],"degree":[10],"at":[11],"least":[12],"$2$":[13],"such":[14],"that":[15,31],"$f-f(0)$":[16],"is":[17],"non-additive.":[18],"For":[19],"$\u03b1,\u03b2$":[20],"in":[21],"an":[22],"algebraically":[23],"closed":[24],"extension":[25],"$L$":[26],"$k$,":[28],"we":[29],"prove":[30],"there":[32],"are":[33,42],"infinitely":[34],"many":[35],"$\u03bb\\in":[36],"L$":[37],"for":[38,59,76],"which":[39],"both":[40],"points":[41],"preperiodic":[43],"under":[44],"$f(X)+\u03bb$":[45],"if":[46,49],"only":[48],"$\u03b1,\u03b2\\in":[50],"k$":[51],"or":[52],"$f(\u03b2)-f(\u03b1)\\in":[53],"E_f$.":[54],"Here":[55],"$E_f=\\{c\\in":[56],"G_f:(f-f(0))^n(c)\\in":[57],"G_f\\text{":[58],"every":[60],"}n\\ge0\\}$,":[61],"where":[62],"$G_f=\\{c\\in":[63],"k":[64],":":[65],"f(X+c)-f(X)\\in":[66],"k\\}$.":[67],"We":[68],"also":[69],"provide":[70],"necessary":[72],"sufficient":[74],"criterion":[75],"the":[77],"corresponding":[78],"colliding":[79],"orbits":[80],"set":[81],"to":[82],"infinite.":[84]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}