{"id":"https://openalex.org/W7220938966","doi":"https://doi.org/10.48550/arxiv.2610.07435","title":"Period spectrum and rigidity of interval maps","display_name":"Period spectrum and rigidity of interval maps","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220938966","doi":"https://doi.org/10.48550/arxiv.2610.07435"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07435","pdf_url":"https://arxiv.org/pdf/2610.07435","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/2610.07435","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053136502","display_name":"Gabriel Fuhrmann","orcid":"https://orcid.org/0000-0002-0634-0802","observed_orcids":["https://orcid.org/0000-0002-0634-0802"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fuhrmann, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074640842","display_name":"Maik Gr\u00f6ger","orcid":"https://orcid.org/0000-0003-0802-8932","observed_orcids":["https://orcid.org/0000-0003-0802-8932"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gr\u00f6ger, Maik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5009428125","display_name":"Alejandro Passeggi","orcid":"https://orcid.org/0009-0001-7996-4800","observed_orcids":["https://orcid.org/0009-0001-7996-4800"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Passeggi, Alejandro","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/T11151","display_name":"Advanced Topology and Set Theory","score":9.999999747378752e-05,"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":9.999999747378752e-05,"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/periodic-orbits","display_name":"periodic orbits","score":0.8190000057220459},{"id":"https://openalex.org/keywords/interval-maps","display_name":"interval maps","score":0.9549999833106995},{"id":"https://openalex.org/keywords/topological-mixing","display_name":"topological mixing","score":0.8169999718666077},{"id":"https://openalex.org/keywords/spectral-decomposition","display_name":"spectral decomposition","score":0.753000020980835},{"id":"https://openalex.org/keywords/basic-sets","display_name":"basic sets","score":0.9750000238418579},{"id":"https://openalex.org/keywords/dense-periodic-points","display_name":"dense periodic points","score":0.6169999837875366},{"id":"https://openalex.org/keywords/one-dimensional-dynamical-systems","display_name":"one-dimensional dynamics","score":0.5720000267028809}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7764000296592712},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7638000249862671},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.7511000037193298},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5394999980926514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.499099999666214},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35569998621940613},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.3122999966144562},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C2991919592","wikidata":"https://www.wikidata.org/wiki/Q170058","display_name":"Continuous map","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07435","pdf_url":"https://arxiv.org/pdf/2610.07435","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.2610.07435","doi":"https://doi.org/10.48550/arxiv.2610.07435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07435","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:2610.07435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07435","pdf_url":"https://arxiv.org/pdf/2610.07435","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220938966.pdf","grobid_xml":"https://content.openalex.org/works/W7220938966.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1568615646"],"related_works":["https://openalex.org/W2042735075","https://openalex.org/W4294577749","https://openalex.org/W4407043649","https://openalex.org/W2073402966","https://openalex.org/W1992135069","https://openalex.org/W1964801086","https://openalex.org/W7097578690","https://openalex.org/W4391631633","https://openalex.org/W2075265306","https://openalex.org/W1505687878"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,37,72,92],"extent":[3],"to":[4,87],"which":[5],"periodic":[6,35,38,93],"orbits":[7,39,94],"determine":[8,19,42],"a":[9,28,59],"one-dimensional":[10],"dynamical":[11],"system.":[12],"In":[13],"particular,":[14],"we":[15,57],"show":[16],"that":[17],"they":[18,45],"every":[20],"topologically":[21],"mixing":[22],"interval":[23,30,77],"map.":[24],"More":[25],"generally,":[26],"for":[27,49,52,65],"non-mixing":[29],"map":[31,78],"$f$":[32],"with":[33],"dense":[34],"points,":[36],"need":[40],"not":[41],"$f$,":[43,79],"but":[44],"always":[46],"do":[47],"so":[48],"$f^2$.":[50],"Finally,":[51],"maps":[53],"on":[54],"compact":[55],"intervals,":[56],"obtain":[58],"local":[60],"version":[61],"of":[62,75,95],"this":[63],"rigidity:":[64],"each":[66],"basic":[67],"set":[68],"$B$":[69,88],"arising":[70],"in":[71],"spectral":[73],"decomposition":[74],"an":[76,82],"there":[80],"exists":[81],"iterate":[83],"$f^q$":[84],"whose":[85],"restriction":[86],"is":[89],"determined":[90],"by":[91],"$f$.":[96]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
