{"id":"https://openalex.org/W2144516883","doi":"https://doi.org/10.20537/nd1103006","title":"Billiard dynamics: a survey with the emphasis on open problems","display_name":"Billiard dynamics: a survey with the emphasis on open problems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2144516883","doi":"https://doi.org/10.20537/nd1103006","mag":"2144516883"},"language":"en","primary_location":{"id":"doi:10.20537/nd1103006","doi":"https://doi.org/10.20537/nd1103006","is_oa":true,"landing_page_url":"https://doi.org/10.20537/nd1103006","pdf_url":"http://nd.ics.org.ru/upload/iblock/8a7/ND_2011_v7_n3_06.pdf","source":{"id":"https://openalex.org/S4210174850","display_name":"Nelineinaya Dinamika","issn_l":"1816-448X","issn":["1816-448X","1817-5155","2658-5316","2658-5324"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nelineinaya Dinamika","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://nd.ics.org.ru/upload/iblock/8a7/ND_2011_v7_n3_06.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090415767","display_name":"Eug\u00e8ne Gutkin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"E. Gutkin","raw_affiliation_strings":["Department of Mathematics Nicolaus Copernicus University Chopina 12/18, 87-100 Torun, Poland;","Poland","IM PAN, Sniadeckich 8, Warszawa 10, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Nicolaus Copernicus University Chopina 12/18, 87-100 Torun, Poland;","institution_ids":["https://openalex.org/I3019271933"]},{"raw_affiliation_string":"Poland","institution_ids":[]},{"raw_affiliation_string":"IM PAN, Sniadeckich 8, Warszawa 10, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090415767"],"corresponding_institution_ids":["https://openalex.org/I3019271933"],"apc_list":null,"apc_paid":null,"fwci":8.3125,"has_fulltext":true,"cited_by_count":54,"citation_normalized_percentile":{"value":0.99000799,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"489","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9663000106811523,"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":0.9663000106811523,"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":0.005499999970197678,"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/T12504","display_name":"Mathematics and Applications","score":0.005200000014156103,"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/billiard-dynamics","display_name":"billiard dynamics","score":0.9739999771118164},{"id":"https://openalex.org/keywords/open-problems","display_name":"open problems","score":0.9729999899864197},{"id":"https://openalex.org/keywords/chaotic-dynamics","display_name":"chaotic dynamics","score":0.4749999940395355},{"id":"https://openalex.org/keywords/integrable-billiards","display_name":"integrable billiards","score":0.6510000228881836},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"ergodic theory","score":0.5109999775886536},{"id":"https://openalex.org/keywords/kam-theory","display_name":"KAM theory","score":0.48500001430511475}],"concepts":[{"id":"https://openalex.org/C193605512","wikidata":"https://www.wikidata.org/wiki/Q2903467","display_name":"Dynamical billiards","level":2,"score":0.8358901739120483},{"id":"https://openalex.org/C177454536","wikidata":"https://www.wikidata.org/wiki/Q578290","display_name":"Emphasis (telecommunications)","level":2,"score":0.8044705986976624},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4829663336277008},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41355347633361816},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33691418170928955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32396361231803894},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.32335424423217773},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1641996204853058},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09508633613586426},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.09323245286941528}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.20537/nd1103006","doi":"https://doi.org/10.20537/nd1103006","is_oa":true,"landing_page_url":"https://doi.org/10.20537/nd1103006","pdf_url":"http://nd.ics.org.ru/upload/iblock/8a7/ND_2011_v7_n3_06.pdf","source":{"id":"https://openalex.org/S4210174850","display_name":"Nelineinaya Dinamika","issn_l":"1816-448X","issn":["1816-448X","1817-5155","2658-5316","2658-5324"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nelineinaya Dinamika","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.20537/nd1103006","doi":"https://doi.org/10.20537/nd1103006","is_oa":true,"landing_page_url":"https://doi.org/10.20537/nd1103006","pdf_url":"http://nd.ics.org.ru/upload/iblock/8a7/ND_2011_v7_n3_06.pdf","source":{"id":"https://openalex.org/S4210174850","display_name":"Nelineinaya Dinamika","issn_l":"1816-448X","issn":["1816-448X","1817-5155","2658-5316","2658-5324"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nelineinaya Dinamika","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2144516883.pdf","grobid_xml":"https://content.openalex.org/works/W2144516883.grobid-xml"},"referenced_works_count":85,"referenced_works":["https://openalex.org/W207450690","https://openalex.org/W355012799","https://openalex.org/W368267856","https://openalex.org/W609406002","https://openalex.org/W1503553685","https://openalex.org/W1506380541","https://openalex.org/W1509894304","https://openalex.org/W1548887510","https://openalex.org/W1561291178","https://openalex.org/W1578664069","https://openalex.org/W1595007535","https://openalex.org/W1595989395","https://openalex.org/W1607950242","https://openalex.org/W1638206340","https://openalex.org/W1969743386","https://openalex.org/W1969810742","https://openalex.org/W1970136394","https://openalex.org/W1970174858","https://openalex.org/W1975269643","https://openalex.org/W1975280011","https://openalex.org/W1978095099","https://openalex.org/W1981185893","https://openalex.org/W1984614267","https://openalex.org/W1987547729","https://openalex.org/W1988372449","https://openalex.org/W1991506399","https://openalex.org/W1993488772","https://openalex.org/W1994978599","https://openalex.org/W1996406379","https://openalex.org/W1998371866","https://openalex.org/W2000367146","https://openalex.org/W2003611370","https://openalex.org/W2004063500","https://openalex.org/W2005186742","https://openalex.org/W2008851703","https://openalex.org/W2019074111","https://openalex.org/W2024810567","https://openalex.org/W2026720219","https://openalex.org/W2029216970","https://openalex.org/W2033103663","https://openalex.org/W2035087672","https://openalex.org/W2039809812","https://openalex.org/W2040635624","https://openalex.org/W2045166668","https://openalex.org/W2047029313","https://openalex.org/W2047942769","https://openalex.org/W2057816390","https://openalex.org/W2068070751","https://openalex.org/W2068993570","https://openalex.org/W2069386321","https://openalex.org/W2070178103","https://openalex.org/W2072554153","https://openalex.org/W2073916476","https://openalex.org/W2074886971","https://openalex.org/W2076907850","https://openalex.org/W2079427440","https://openalex.org/W2079694968","https://openalex.org/W2081300190","https://openalex.org/W2081339264","https://openalex.org/W2081817659","https://openalex.org/W2083048522","https://openalex.org/W2085772715","https://openalex.org/W2088834857","https://openalex.org/W2092265508","https://openalex.org/W2095165504","https://openalex.org/W2103022361","https://openalex.org/W2103417611","https://openalex.org/W2110584684","https://openalex.org/W2117139546","https://openalex.org/W2131087180","https://openalex.org/W2144653303","https://openalex.org/W2169048238","https://openalex.org/W2186926958","https://openalex.org/W2275895860","https://openalex.org/W2313225059","https://openalex.org/W2322864499","https://openalex.org/W2324853665","https://openalex.org/W2495311361","https://openalex.org/W2504846205","https://openalex.org/W2962850301","https://openalex.org/W3105522039","https://openalex.org/W3175367423","https://openalex.org/W4205302990","https://openalex.org/W4243179348","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W2033460686","https://openalex.org/W7100832464","https://openalex.org/W4212774705","https://openalex.org/W7162402495","https://openalex.org/W2332941705","https://openalex.org/W1992866576","https://openalex.org/W2323201233","https://openalex.org/W7100504206","https://openalex.org/W2945271505","https://openalex.org/W2169922485"],"abstract_inverted_index":{"\u0414\u0438\u043d\u0430\u043c\u0438\u043a\u0430":[0],"\u0431\u0438\u043b\u043b\u0438\u0430\u0440\u0434a:":[1],"\u043e\u0431\u0437\u043e\u0440\u043d\u0430\u044f":[2],"\u0441\u0442\u0430\u0442\u044c\u044f":[3],"\u0441":[4],"\u0430\u043a\u0446\u0435\u043d\u0442\u043e\u043c":[5],"\u043d\u0430":[6],"\u043d\u0435\u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435":[7],"\u0437\u0430\u0434\u0430\u0447\u0438":[8],"\u0415":[9]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":16}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}