{"id":"https://openalex.org/W7213420067","doi":"https://doi.org/10.48550/arxiv.2609.16241","title":"Infinitesimal dynamical spectral rigidity of the Bunimovich stadium","display_name":"Infinitesimal dynamical spectral rigidity of the Bunimovich stadium","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213420067","doi":"https://doi.org/10.48550/arxiv.2609.16241"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16241","pdf_url":"https://arxiv.org/pdf/2609.16241","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/2609.16241","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151880715","display_name":"Xianghui Shi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shi, Xianghui","raw_affiliation_strings":["Department of Mathematics , University of California , Los Angeles , 520 Portola Plaza , Los Angeles , CA 90095 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of California , Los Angeles , 520 Portola Plaza , Los Angeles , CA 90095 , USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5151880715"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9057999849319458,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9057999849319458,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.04560000076889992,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.024900000542402267,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bunimovich-stadium","display_name":"Bunimovich stadium","score":0.953000009059906},{"id":"https://openalex.org/keywords/length-spectrum","display_name":"length spectrum","score":0.9139999747276306},{"id":"https://openalex.org/keywords/deformation-function","display_name":"deformation function","score":0.7149999737739563},{"id":"https://openalex.org/keywords/strictly-convex-domains","display_name":"strictly convex domains","score":0.5059999823570251},{"id":"https://openalex.org/keywords/reflection-symmetry","display_name":"reflection symmetry","score":0.6460000276565552},{"id":"https://openalex.org/keywords/billiards","display_name":"billiards","score":0.3409999907016754}],"concepts":[{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.7567999958992004},{"id":"https://openalex.org/C2778539849","wikidata":"https://www.wikidata.org/wiki/Q7596467","display_name":"Stadium","level":2,"score":0.6938999891281128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6334999799728394},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6133000254631042},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48260000348091125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47909998893737793},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C155759531","wikidata":"https://www.wikidata.org/wiki/Q7625050","display_name":"Structural rigidity","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2644999921321869}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16241","pdf_url":"https://arxiv.org/pdf/2609.16241","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.2609.16241","doi":"https://doi.org/10.48550/arxiv.2609.16241","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16241","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:2609.16241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16241","pdf_url":"https://arxiv.org/pdf/2609.16241","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":[{"id":"https://openalex.org/F4320315473","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541"},{"id":"https://openalex.org/F4320324720","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213420067.pdf","grobid_xml":"https://content.openalex.org/works/W7213420067.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4402511113","https://openalex.org/W4416770141"],"related_works":["https://openalex.org/W2413283357","https://openalex.org/W2618236342","https://openalex.org/W4416770141","https://openalex.org/W2951131126","https://openalex.org/W1486815857","https://openalex.org/W7100075303","https://openalex.org/W3034816656","https://openalex.org/W3205536009","https://openalex.org/W3040453921","https://openalex.org/W2622592483"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,8,18,40,44,59,62,70,80],"infinitesimal":[3],"dynamical":[4],"spectral":[5],"rigidity":[6],"of":[7,20,77,83],"circular":[9,27],"Bunimovich":[10],"stadium":[11,60,71],"with":[12,29],"sufficiently":[13],"long":[14],"flat":[15,45,75],"edges,":[16],"in":[17,54],"class":[19,56],"domains":[21],"obtained":[22],"by":[23],"replacing":[24],"its":[25,36,66],"two":[26],"arcs":[28,33],"strictly":[30],"convex":[31],"$C^{4}$":[32],"and":[34],"keeping":[35],"reflection":[37],"symmetry":[38],"across":[39],"axis":[41],"parallel":[42],"to":[43],"edges.":[46],"That":[47],"is,":[48],"if":[49],"a":[50,88],"$C^{1}$":[51],"one-parameter":[52],"family":[53],"this":[55],"passing":[57],"through":[58],"preserves":[61],"length":[63],"spectrum,":[64],"then":[65],"deformation":[67,81],"function":[68],"at":[69],"vanishes":[72],"identically.":[73],"For":[74],"edges":[76],"arbitrary":[78],"length,":[79],"functions":[82],"such":[84],"families":[85],"still":[86],"span":[87],"finite-dimensional":[89],"space.":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}
