{"id":"https://openalex.org/W7223128758","doi":"https://doi.org/10.48550/arxiv.2610.27796","title":"Absolute winning properties of exceptional sets for rational maps","display_name":"Absolute winning properties of exceptional sets for rational maps","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223128758","doi":"https://doi.org/10.48550/arxiv.2610.27796"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27796","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27796","pdf_url":"https://arxiv.org/pdf/2610.27796","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/2610.27796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133363199","display_name":"Haoyang Ji","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ji, Haoyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133363199"],"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":0.9994999766349792,"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":0.9994999766349792,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.00019999999494757503,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/julia-sets","display_name":"Julia sets","score":0.7549999952316284},{"id":"https://openalex.org/keywords/rational-maps","display_name":"rational maps","score":0.8840000033378601},{"id":"https://openalex.org/keywords/weak-hyperbolicity","display_name":"weak hyperbolicity","score":0.8209999799728394},{"id":"https://openalex.org/keywords/exceptional-sets","display_name":"exceptional sets","score":0.9010000228881836},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.8519999980926514},{"id":"https://openalex.org/keywords/potential-games","display_name":"potential games","score":0.6700000166893005},{"id":"https://openalex.org/keywords/uniform-expansion","display_name":"uniform expansion","score":0.9269999861717224},{"id":"https://openalex.org/keywords/diophantine-approximation","display_name":"Diophantine approximation","score":0.8610000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.75},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6388999819755554},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5773000121116638},{"id":"https://openalex.org/C2777487392","wikidata":"https://www.wikidata.org/wiki/Q481201","display_name":"Absolute (philosophy)","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49470001459121704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3564999997615814},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34279999136924744},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26260000467300415}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27796","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27796","pdf_url":"https://arxiv.org/pdf/2610.27796","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.2610.27796","doi":"https://doi.org/10.48550/arxiv.2610.27796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27796","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:2610.27796","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27796","pdf_url":"https://arxiv.org/pdf/2610.27796","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/G1662001357","display_name":null,"funder_award_id":"12301103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223128758.pdf","grobid_xml":"https://content.openalex.org/works/W7223128758.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7167907338"],"related_works":["https://openalex.org/W7167907338","https://openalex.org/W2990754323","https://openalex.org/W2149057882","https://openalex.org/W7096228561","https://openalex.org/W2084542492","https://openalex.org/W2110606777","https://openalex.org/W4280622058","https://openalex.org/W1576198646","https://openalex.org/W3143230502","https://openalex.org/W2298954919"],"abstract_inverted_index":{"We":[0,37],"study":[1],"Schmidt's":[2],"game":[3,73],"on":[4,44],"the":[5,22,57,62,67,82],"Julia":[6],"set":[7,23,64],"$J(f)$":[8,27,45],"of":[9,24],"weak":[10],"hyperbolic":[11],"rational":[12],"maps":[13],"$f:\\CC\\to\\CC$.":[14],"For":[15],"each":[16,47,85],"$y\\in":[17],"J(f)$,":[18],"let":[19],"$E(f,y)$":[20,40],"be":[21],"points":[25,69],"in":[26],"whose":[28],"forward":[29],"orbits":[30],"stay":[31],"a":[32,71],"positive":[33],"distance":[34],"from":[35],"$y$.":[36,88],"prove":[38,56],"that":[39],"is":[41],"absolute":[42,58],"winning":[43,59],"for":[46,61,84],"$y":[48],"\\in":[49],"J(f)$.":[50],"To":[51],"do":[52],"this,":[53],"we":[54],"first":[55],"property":[60],"exceptional":[63],"associated":[65],"to":[66,80],"critical":[68],"by":[70],"potential":[72],"argument,":[74],"and":[75],"then":[76],"use":[77],"uniform":[78],"expansion":[79],"obtain":[81],"result":[83],"target":[86],"point":[87]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}
