{"id":"https://openalex.org/W7204864734","doi":"https://doi.org/10.48550/arxiv.2608.31132","title":"Robustness of topological entropy under small area deformations","display_name":"Robustness of topological entropy under small area deformations","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204864734","doi":"https://doi.org/10.48550/arxiv.2608.31132"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.31132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31132","pdf_url":"https://arxiv.org/pdf/2608.31132","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/2608.31132","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073884334","display_name":"Marcelo R. R. Alves","orcid":"https://orcid.org/0000-0003-4811-4990","observed_orcids":["https://orcid.org/0000-0003-4811-4990"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alves, Marcelo R. R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070174463","display_name":"Matthias Meiwes","orcid":"https://orcid.org/0000-0001-5589-6586","observed_orcids":["https://orcid.org/0000-0001-5589-6586"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meiwes, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109605109","display_name":"Beomjun Sohn","orcid":"https://orcid.org/0000-0002-3394-0360","observed_orcids":["https://orcid.org/0000-0002-3394-0360"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sohn, Beomjun","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":0.9740999937057495,"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":0.9740999937057495,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.020600000396370888,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/topological-entropy","display_name":"topological entropy","score":1.0},{"id":"https://openalex.org/keywords/hamiltonian-diffeomorphisms","display_name":"Hamiltonian diffeomorphisms","score":0.9900000095367432},{"id":"https://openalex.org/keywords/closed-surfaces","display_name":"closed surfaces","score":0.796999990940094},{"id":"https://openalex.org/keywords/spectral-distance","display_name":"spectral distance","score":0.9909999966621399},{"id":"https://openalex.org/keywords/entropy-stability","display_name":"entropy stability","score":0.36899998784065247}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.7967000007629395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7010999917984009},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.6022999882698059},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.40880000591278076},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3720000088214874},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2939999997615814},{"id":"https://openalex.org/C155673373","wikidata":"https://www.wikidata.org/wiki/Q1648886","display_name":"Structural stability","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.2603999972343445},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.31132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31132","pdf_url":"https://arxiv.org/pdf/2608.31132","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.2608.31132","doi":"https://doi.org/10.48550/arxiv.2608.31132","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31132","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.31132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31132","pdf_url":"https://arxiv.org/pdf/2608.31132","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/G1966264416","display_name":null,"funder_award_id":"NRF\u20102020R1A5A1016126","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G1968833158","display_name":"The topological entropy of Reeb flows and its relations to symplectic topology","funder_award_id":"1286921N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G2802873701","display_name":null,"funder_award_id":"RS\u20102023\u201000211186","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G3033566463","display_name":null,"funder_award_id":"2020R1A5A1016126","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G8868332474","display_name":null,"funder_award_id":"541525489","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204864734.pdf","grobid_xml":"https://content.openalex.org/works/W7204864734.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W3213509598","https://openalex.org/W4393212735","https://openalex.org/W4399418151","https://openalex.org/W4403346501","https://openalex.org/W4412152419","https://openalex.org/W4413185141"],"related_works":["https://openalex.org/W4413185141","https://openalex.org/W4402269993","https://openalex.org/W2606965088","https://openalex.org/W7043837398","https://openalex.org/W7214744008","https://openalex.org/W2998816237","https://openalex.org/W3213509598","https://openalex.org/W2962809805","https://openalex.org/W1976395442","https://openalex.org/W2108301832"],"abstract_inverted_index":{"In":[0,78],"this":[1,111],"paper,":[2],"we":[3,38],"establish":[4],"a":[5,22,32,63,67],"new":[6,105],"type":[7],"of":[8,15,18,36,70,73,98],"stability":[9,107],"phenomenon":[10],"for":[11,41,54],"the":[12,104,116],"topological":[13],"entropy":[14,90],"Hamiltonian":[16,33,56],"diffeomorphisms":[17],"closed":[19,23],"surfaces.":[20],"For":[21],"surface":[24],"endowed":[25],"with":[26,113],"an":[27,92],"area":[28,74],"form":[29],"$(\u03a3,\u03c9)$":[30],"and":[31],"diffeomorphism":[34,57],"$\u03d5$":[35,61,83],"$(\u03a3,\u03c9)$,":[37],"show":[39],"that":[40,48],"every":[42,55],"$\\varepsilon>0$":[43],"there":[44],"exists":[45],"$A=A(\u03d5,\\varepsilon)>0$":[46],"such":[47],"\\[":[49],"h_{\\mathrm{top}}(\u03d5')":[50],">":[51],"h_{\\mathrm{top}}(\u03d5)-\\varepsilon":[52],"\\]":[53],"$\u03d5'$":[58],"obtained":[59],"from":[60,103],"by":[62,91,121],"deformation":[64,94],"supported":[65,95],"in":[66,96,110],"disjoint":[68],"union":[69],"disks,":[71],"each":[72],"less":[75],"than":[76],"$A$.":[77],"particular,":[79],"if":[80],"$h_{\\mathrm{top}}(\u03d5)>0$,":[81],"then":[82],"cannot":[84],"be":[85],"made":[86],"to":[87,115],"have":[88],"zero":[89],"area-preserving":[93],"disks":[97],"small":[99],"area.":[100],"This":[101],"follows":[102],"braid":[106],"result":[108],"established":[109],"paper":[112],"respect":[114],"spectral":[117],"distance":[118],"recently":[119],"introduced":[120],"Connery-Grigg.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}