{"id":"https://openalex.org/W1992980668","doi":"https://doi.org/10.1080/10586458.1997.10504601","title":"Hausdorff Convergence and the Limit Shape of the Unicorns","display_name":"Hausdorff Convergence and the Limit Shape of the Unicorns","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1992980668","doi":"https://doi.org/10.1080/10586458.1997.10504601","mag":"1992980668"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1997.10504601","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.1997.10504601","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.1997.10504601","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.1997.10504601","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072817844","display_name":"Bernd Krauskopf","orcid":"https://orcid.org/0000-0002-8940-230X"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bernd Krauskopf","raw_affiliation_strings":["Vakgroep Theoretische Natuurkunde, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands E-mail: berndk@nat.vu.nl berndk@cam.comell.edu","Atoms, Molecules, Lasers"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vakgroep Theoretische Natuurkunde, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands E-mail: berndk@nat.vu.nl berndk@cam.comell.edu","institution_ids":["https://openalex.org/I865915315"]},{"raw_affiliation_string":"Atoms, Molecules, Lasers","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069586927","display_name":"Hartje Kriete","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hartje Kriete","raw_affiliation_strings":["Mathematisches Institut, Georg-August Universit\u00e4t, 37073, Gottingen, Germany E-mail: kriete@cfgauss.uni-math.gwdg.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Georg-August Universit\u00e4t, 37073, Gottingen, Germany E-mail: kriete@cfgauss.uni-math.gwdg.de","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5791,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58662982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":"2","first_page":"117","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9876999855041504,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9678999781608582,"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/mathematics","display_name":"Mathematics","score":0.896404504776001},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6838746666908264},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6744830012321472},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.5808420181274414},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5706743597984314},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.5389133095741272},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4783598780632019},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.45777106285095215},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.4348636865615845},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.42485401034355164},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3738831877708435},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16010543704032898}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.896404504776001},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6838746666908264},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6744830012321472},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.5808420181274414},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5706743597984314},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.5389133095741272},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4783598780632019},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.45777106285095215},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.4348636865615845},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.42485401034355164},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3738831877708435},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16010543704032898},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10586458.1997.10504601","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.1997.10504601","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.1997.10504601","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/2f8e32ee-d7a2-4202-a291-a20013fd094a","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/2f8e32ee-d7a2-4202-a291-a20013fd094a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Krauskopf, B & Kriete, H 1997, 'Hausdorff convergence and the limit shape of the unicorns', Experimental Mathematics, vol. 6(2), pp. 117 - 135.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CULeuclid:euclid.em/1047649999","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1047649999","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/e918b18d-3463-49b2-a0ad-7a16cc44d8cf","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/e918b18d-3463-49b2-a0ad-7a16cc44d8cf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B & Kriete, H 1997, 'Hausdorff convergence and the limit shape of the unicorns.', Experimental Mathematics, vol. 6, no. 2, pp. 117-135. https://doi.org/10.1080/10586458.1997.10504601","raw_type":"article"},{"id":"pmh:oai:research.vu.nl:publications/e918b18d-3463-49b2-a0ad-7a16cc44d8cf","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/e918b18d-3463-49b2-a0ad-7a16cc44d8cf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B & Kriete, H 1997, 'Hausdorff convergence and the limit shape of the unicorns.', Experimental Mathematics, vol. 6, no. 2, pp. 117-135. https://doi.org/10.1080/10586458.1997.10504601","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/10586458.1997.10504601","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.1997.10504601","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.1997.10504601","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1992980668.pdf","grobid_xml":"https://content.openalex.org/works/W1992980668.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1578418738","https://openalex.org/W1646303234","https://openalex.org/W1695890003","https://openalex.org/W1970071682","https://openalex.org/W1995297510","https://openalex.org/W2012376049","https://openalex.org/W2013150548","https://openalex.org/W2056966260","https://openalex.org/W2059998776","https://openalex.org/W2065629179","https://openalex.org/W2069994471","https://openalex.org/W2072386919","https://openalex.org/W2076969890","https://openalex.org/W2084372123","https://openalex.org/W2095047249","https://openalex.org/W2109935497","https://openalex.org/W2156093760","https://openalex.org/W3102739121","https://openalex.org/W4231258329","https://openalex.org/W4241933253","https://openalex.org/W4253111115"],"related_works":["https://openalex.org/W2367466578","https://openalex.org/W4298092961","https://openalex.org/W2951586668","https://openalex.org/W4294017991","https://openalex.org/W2886349793","https://openalex.org/W1144450175","https://openalex.org/W2031465436","https://openalex.org/W1512585147","https://openalex.org/W1991371429","https://openalex.org/W4298141576"],"abstract_inverted_index":{"We":[0],"discuss":[1],"the":[2,50,60,68,72],"Hausdorff":[3],"convergence":[4,24,51],"of":[5,15,52,71],"hyperbolic":[6],"components":[7],"in":[8,34],"parameter":[9],"space":[10],"as":[11],"a":[12,35],"one-parameter":[13],"family":[14],"transcendental":[16],"functions":[17],"is":[18,25,32,39],"dynamically":[19],"approximated":[20],"by":[21,28],"polynomials.":[22],"This":[23],"strongly":[26],"suggested":[27],"computer":[29],"experiments":[30],"and":[31,44],"proved":[33],"weaker":[36],"form,":[37],"which":[38,63],"illustrated":[40],"with":[41],"exponential,":[42],"sine":[43],"cosine":[45],"families.":[46],"Furthermore,":[47],"we":[48],"consider":[49],"subhyperbolic":[53],"components.":[54],"Our":[55],"result":[56],"also":[57],"applies":[58],"to":[59,66],"antiholomorphic":[61],"exponentials,":[62],"allows":[64],"us":[65],"investigate":[67],"limit":[69],"shape":[70],"unicorns.":[73]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
