{"id":"https://openalex.org/W7204911787","doi":"https://doi.org/10.48550/arxiv.2608.30965","title":"Higher genus Cherry flows and full families of GIETs","display_name":"Higher genus Cherry flows and full families of GIETs","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204911787","doi":"https://doi.org/10.48550/arxiv.2608.30965"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30965","pdf_url":"https://arxiv.org/pdf/2608.30965","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/2608.30965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051896764","display_name":"Luca Marchese","orcid":"https://orcid.org/0000-0002-6588-2871","observed_orcids":["https://orcid.org/0000-0002-6588-2871"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marchese, Luca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022582778","display_name":"Liviana Palmisano","orcid":"https://orcid.org/0000-0001-5741-2303","observed_orcids":["https://orcid.org/0000-0001-5741-2303"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Palmisano, Liviana","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":0.9994999766349792,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","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/T11151","display_name":"Advanced Topology and Set Theory","score":0.0,"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/higher-genus","display_name":"higher genus","score":0.4440000057220459},{"id":"https://openalex.org/keywords/full-families","display_name":"full families","score":0.6349999904632568},{"id":"https://openalex.org/keywords/semi-conjugacy","display_name":"semi-conjugacy","score":0.8830000162124634},{"id":"https://openalex.org/keywords/ergodic-measures","display_name":"ergodic measures","score":0.8450000286102295},{"id":"https://openalex.org/keywords/recurrent-dynamics","display_name":"recurrent dynamics","score":0.671999990940094},{"id":"https://openalex.org/keywords/two-dimensional-torus","display_name":"two-dimensional torus","score":0.7289999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8055999875068665},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5618000030517578},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5033000111579895},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4002000093460083},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3562999963760376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34790000319480896},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30965","pdf_url":"https://arxiv.org/pdf/2608.30965","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.2608.30965","doi":"https://doi.org/10.48550/arxiv.2608.30965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30965","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:2608.30965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30965","pdf_url":"https://arxiv.org/pdf/2608.30965","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204911787.pdf","grobid_xml":"https://content.openalex.org/works/W7204911787.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2679966894","https://openalex.org/W4416904138","https://openalex.org/W7160662828"],"related_works":["https://openalex.org/W2766956791","https://openalex.org/W4388043898","https://openalex.org/W4416904138","https://openalex.org/W3168776236","https://openalex.org/W7213301812","https://openalex.org/W2522882468","https://openalex.org/W1984445827","https://openalex.org/W6910785573","https://openalex.org/W4311310488","https://openalex.org/W7164762964"],"abstract_inverted_index":{"Cherry":[0,61,79],"flows":[1,7,27],"are":[2,56],"classical":[3],"examples":[4],"of":[5,26,108,123],"$C^\\infty$":[6,23],"on":[8,94],"the":[9,52,106,120],"two-dimensional":[10],"torus":[11],"exhibiting":[12],"non-trivial":[13],"recurrent":[14],"dynamics.":[15],"For":[16],"every":[17,46,109],"genus":[18],"$g\\geq1$":[19],"we":[20],"construct":[21],"a":[22,33,60,78,95,115],"parameter":[24],"family":[25,76,118],"whose":[28,63,81],"first":[29],"return":[30,64],"map":[31,65],"is":[32,66],"generalized":[34],"interval":[35,47],"exchange":[36,48],"transformation":[37,49],"(GIET)":[38],"with":[39,101,119],"flat":[40,102],"pieces.":[41],"In":[42,70],"such":[43],"family,":[44],"for":[45,72,99],"$T$":[50],"satisfying":[51],"Keane":[53],"property,":[54],"there":[55],"parameters":[57],"corresponding":[58],"to":[59,68],"flow":[62,80],"semi-conjugate":[67],"$T$.":[69],"particular,":[71],"each":[73],"$k=1,\\ldots,g$,":[74],"our":[75],"contains":[77],"unique":[82],"quasi-minimal":[83],"set":[84],"supports":[85],"exactly":[86],"$k$":[87],"ergodic":[88],"invariant":[89],"measures.":[90],"The":[91],"construction":[92],"relies":[93],"Full":[96],"Family":[97],"Theorem":[98],"GIETs":[100],"pieces,":[103],"which":[104],"establishes":[105],"realization":[107],"admissible":[110],"Rauzy":[111],"renormalization":[112],"path":[113],"within":[114],"specific":[116],"finite-dimensional":[117],"optimal":[121],"number":[122],"parameters.":[124]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-02T00:00:00"}
