{"id":"https://openalex.org/W1978585161","doi":"https://doi.org/10.3390/e12040953","title":"Entropy of Bounding Tori","display_name":"Entropy of Bounding Tori","publication_year":2010,"publication_date":"2010-04-15","ids":{"openalex":"https://openalex.org/W1978585161","doi":"https://doi.org/10.3390/e12040953","mag":"1978585161"},"language":"en","primary_location":{"id":"doi:10.3390/e12040953","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e12040953","pdf_url":"https://www.mdpi.com/1099-4300/12/4/953/pdf?version=1424784734","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/12/4/953/pdf?version=1424784734","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089719253","display_name":"Jacob Katriel","orcid":"https://orcid.org/0000-0002-0846-4868"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Jacob Katriel","raw_affiliation_strings":["Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113802292","display_name":"Robert Gilmore","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Gilmore","raw_affiliation_strings":["Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA"],"affiliations":[{"raw_affiliation_string":"Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089719253"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4032,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52872558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"4","first_page":"953","last_page":"960"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9955000281333923,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9897000193595886,"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/torus","display_name":"Torus","score":0.8754820227622986},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7588552236557007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.616935133934021},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5785160660743713},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38589343428611755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3278483748435974},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20030689239501953},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16987481713294983},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13708901405334473}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.8754820227622986},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7588552236557007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.616935133934021},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5785160660743713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38589343428611755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3278483748435974},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20030689239501953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16987481713294983},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13708901405334473},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/e12040953","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e12040953","pdf_url":"https://www.mdpi.com/1099-4300/12/4/953/pdf?version=1424784734","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a3be0471655e486ca39309f1ab29d20b","is_oa":true,"landing_page_url":"https://doaj.org/article/a3be0471655e486ca39309f1ab29d20b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 12, Iss 4, Pp 953-960 (2010)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e12040953","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e12040953","pdf_url":"https://www.mdpi.com/1099-4300/12/4/953/pdf?version=1424784734","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1978585161.pdf","grobid_xml":"https://content.openalex.org/works/W1978585161.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1964840403","https://openalex.org/W1967797812","https://openalex.org/W1978757958","https://openalex.org/W1980641511","https://openalex.org/W2014278554","https://openalex.org/W2052456444","https://openalex.org/W2076174416","https://openalex.org/W2076577342","https://openalex.org/W2087041896","https://openalex.org/W2090439465","https://openalex.org/W4238086151","https://openalex.org/W4249024780","https://openalex.org/W4253904265"],"related_works":["https://openalex.org/W2960434112","https://openalex.org/W3049714198","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W2049158118","https://openalex.org/W1499880030","https://openalex.org/W4205994410","https://openalex.org/W2123827981","https://openalex.org/W2538665745","https://openalex.org/W2788195450"],"abstract_inverted_index":{"Branched":[0],"manifolds":[1],"that":[2,37,56],"describe":[3],"strange":[4],"attractors":[5],"in":[6],"R3":[7],"can":[8],"be":[9],"enclosed":[10],"in,":[11],"and":[12],"are":[13,23],"organized":[14],"by,":[15],"canonical":[16,42],"bounding":[17,43],"tori.":[18],"Tori":[19],"of":[20,32,40],"genus":[21],"g":[22],"labeled":[24],"by":[25],"a":[26],"symbol":[27],"sequence,":[28],"or":[29],"\u201cperiodic":[30],"orbit\u201d,":[31],"period":[33],"g-1.":[34],"We":[35],"show":[36],"the":[38,57],"number":[39],"distinct":[41],"tori":[44,59],"grows":[45],"exponentially":[46],"like":[47],"N(g)":[48],"~":[49],"e\u03b3(g-1),":[50],"with":[51],"e\u03b3":[52],"=":[53],"3,":[54],"so":[55],"\u201cbounding":[58],"entropy\u201d":[60],"is":[61],"log(3).":[62]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}