{"id":"https://openalex.org/W1996946577","doi":"https://doi.org/10.1142/s0218127408021555","title":"AN IRREVERSIBLE PROCESS REPRESENTED BY A REVERSIBLE ONE","display_name":"AN IRREVERSIBLE PROCESS REPRESENTED BY A REVERSIBLE ONE","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W1996946577","doi":"https://doi.org/10.1142/s0218127408021555","mag":"1996946577"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408021555","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408021555","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","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/A5108467785","display_name":"Abraham Boyarsky","orcid":null},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"ABRAHAM BOYARSKY","raw_affiliation_strings":["Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada","Department of Mathematics and Statistics , Concordia University , 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , Concordia University , 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102002346","display_name":"Pawe\u0142 G\u00f3ra","orcid":"https://orcid.org/0000-0002-1577-8160"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"PAWE\u0141 G\u00d3RA","raw_affiliation_strings":["Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada","Department of Mathematics and Statistics , Concordia University , 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , Concordia University , 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I60158472"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0694916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"07","first_page":"2059","last_page":"2061"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.8116156458854675},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7130799293518066},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5557124018669128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5462145805358887},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5401083827018738},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5371423959732056},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5321530103683472},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.529682993888855},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4657842218875885},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4385698437690735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.321868896484375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27100670337677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23964133858680725},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23126175999641418},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.139004647731781},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10409638285636902},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0867648720741272}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.8116156458854675},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7130799293518066},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5557124018669128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5462145805358887},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5401083827018738},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5371423959732056},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5321530103683472},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.529682993888855},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4657842218875885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4385698437690735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.321868896484375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27100670337677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23964133858680725},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23126175999641418},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.139004647731781},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10409638285636902},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0867648720741272},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127408021555","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408021555","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W208033356","https://openalex.org/W1965129767","https://openalex.org/W2043320933","https://openalex.org/W4247385211"],"related_works":["https://openalex.org/W2004708907","https://openalex.org/W2377429601","https://openalex.org/W2386043911","https://openalex.org/W3171270255","https://openalex.org/W2368252804","https://openalex.org/W3003512042","https://openalex.org/W2379367191","https://openalex.org/W2352594230","https://openalex.org/W2380540883","https://openalex.org/W1555078768"],"abstract_inverted_index":{"Chaotic":[0],"maps":[1],"on":[2,93],"an":[3,105],"interval":[4],"are":[5,37],"irreversible":[6],"in":[7,111],"the":[8,32,35,44,73,112],"sense":[9],"that":[10,71],"trajectories":[11,22],"of":[12,23,95],"points":[13],"cannot":[14],"be":[15,49],"reversed.":[16],"Furthermore,":[17],"even":[18],"when":[19],"one":[20],"considers":[21],"probabilities":[24],"or":[25],"probability":[26],"density":[27],"functions":[28],"(pdf)":[29],"generated":[30],"by":[31],"chaotic":[33,51],"map,":[34],"processes":[36],"irreversible.":[38],"In":[39],"this":[40,109],"note":[41],"we":[42,79],"consider":[43],"following":[45],"question:":[46],"let":[47],"\u03c4":[48],"a":[50,55,60,68,81],"map":[52],"which":[53,84,107],"takes":[54,85],"pdf":[56,61],"f":[57,62,86,89,97,100],"0":[58,87,101],"to":[59,88,99],"1":[63,90,98],".":[64,102],"Does":[65],"there":[66],"exist":[67],"reversible":[69],"process":[70],"accomplishes":[72],"same":[74],"thing.":[75],"For":[76],"example,":[77],"can":[78],"construct":[80],"differential":[82],"equation":[83],"and":[91],"then,":[92],"reversal":[94],"time,":[96],"We":[103],"present":[104],"example":[106],"answers":[108],"question":[110],"affirmative.":[113]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}