{"id":"https://openalex.org/W51588023","doi":"https://doi.org/10.1007/978-3-540-95972-4_2","title":"Computational Methods for Rigorous Analysis of Chaotic Systems","display_name":"Computational Methods for Rigorous Analysis of Chaotic Systems","publication_year":2009,"publication_date":"2009-02-02","ids":{"openalex":"https://openalex.org/W51588023","doi":"https://doi.org/10.1007/978-3-540-95972-4_2","mag":"51588023"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-95972-4_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-95972-4_2","pdf_url":null,"source":{"id":"https://openalex.org/S2764461748","display_name":"Studies in computational intelligence","issn_l":"1860-949X","issn":["1860-949X","1860-9503"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Computational Intelligence","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037161015","display_name":"Zbigniew Galias","orcid":"https://orcid.org/0000-0001-7253-7075"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Zbigniew Galias","raw_affiliation_strings":["AGH University of Science and Technology , Krakow, Poland","Department of Electrical Engineering, AGH University of Science and Technology,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology , Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Electrical Engineering, AGH University of Science and Technology,","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037161015"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.01932115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"25","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9972000122070312,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9950000047683716,"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":0.9902999997138977,"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/attractor","display_name":"Attractor","score":0.7215983867645264},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7204095721244812},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.6031059622764587},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5704881548881531},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.570309579372406},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5439249873161316},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5057401657104492},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5031775832176208},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.5026752948760986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4747900366783142},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46590954065322876},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.4647971987724304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45020192861557007},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4487529993057251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43872296810150146},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4322892427444458},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4193423390388489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1869221329689026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1809822916984558},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09129393100738525}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7215983867645264},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7204095721244812},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.6031059622764587},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5704881548881531},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.570309579372406},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5439249873161316},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5057401657104492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5031775832176208},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.5026752948760986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4747900366783142},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46590954065322876},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.4647971987724304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45020192861557007},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4487529993057251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43872296810150146},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4322892427444458},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4193423390388489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1869221329689026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1809822916984558},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09129393100738525},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-95972-4_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-95972-4_2","pdf_url":null,"source":{"id":"https://openalex.org/S2764461748","display_name":"Studies in computational intelligence","issn_l":"1860-949X","issn":["1860-949X","1860-9503"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Computational Intelligence","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W22096500","https://openalex.org/W175617483","https://openalex.org/W401634476","https://openalex.org/W616348928","https://openalex.org/W1483874187","https://openalex.org/W1493455171","https://openalex.org/W1574303240","https://openalex.org/W1580809199","https://openalex.org/W1589876408","https://openalex.org/W1964154886","https://openalex.org/W1966278929","https://openalex.org/W1976022108","https://openalex.org/W1982132919","https://openalex.org/W1996419866","https://openalex.org/W1997075911","https://openalex.org/W1999110501","https://openalex.org/W2001659478","https://openalex.org/W2002942449","https://openalex.org/W2009428260","https://openalex.org/W2011687450","https://openalex.org/W2015689071","https://openalex.org/W2016173714","https://openalex.org/W2016299043","https://openalex.org/W2017502732","https://openalex.org/W2019398782","https://openalex.org/W2030170144","https://openalex.org/W2035660588","https://openalex.org/W2044502494","https://openalex.org/W2051110650","https://openalex.org/W2055707808","https://openalex.org/W2055945485","https://openalex.org/W2060924166","https://openalex.org/W2075265306","https://openalex.org/W2077157707","https://openalex.org/W2080029971","https://openalex.org/W2082172869","https://openalex.org/W2097807715","https://openalex.org/W2112602754","https://openalex.org/W2112799776","https://openalex.org/W2125566231","https://openalex.org/W2149363410","https://openalex.org/W2314240464","https://openalex.org/W2479599805","https://openalex.org/W2596598149","https://openalex.org/W2798405286","https://openalex.org/W3109381375","https://openalex.org/W3185484028","https://openalex.org/W4206215385","https://openalex.org/W4242085720","https://openalex.org/W4255338393","https://openalex.org/W4300506249"],"related_works":["https://openalex.org/W4220780102","https://openalex.org/W2410881844","https://openalex.org/W3196334750","https://openalex.org/W1502401885","https://openalex.org/W2004257129","https://openalex.org/W2116281088","https://openalex.org/W2770002227","https://openalex.org/W3039927303","https://openalex.org/W1496637154","https://openalex.org/W1989339867"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}
