{"id":"https://openalex.org/W2963230478","doi":"https://doi.org/10.3934/dcds.2011.31.1197","title":"On the regularization of the collision solutions of the one-center problem with weak forces","display_name":"On the regularization of the collision solutions of the one-center problem with weak forces","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2963230478","doi":"https://doi.org/10.3934/dcds.2011.31.1197","mag":"2963230478"},"language":"en","primary_location":{"id":"doi:10.3934/dcds.2011.31.1197","doi":"https://doi.org/10.3934/dcds.2011.31.1197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/dcds.2011.31.1197","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=482741e0-602e-4ae0-ae75-d9ffbbf86015","source":{"id":"https://openalex.org/S19392275","display_name":"Discrete and Continuous Dynamical Systems","issn_l":"1078-0947","issn":["1078-0947","1553-5231"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Continuous Dynamical Systems","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=482741e0-602e-4ae0-ae75-d9ffbbf86015","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025827755","display_name":"Roberto Castelli","orcid":"https://orcid.org/0000-0002-6805-3956","observed_orcids":["https://orcid.org/0000-0002-6805-3956"]},"institutions":[{"id":"https://openalex.org/I2802176441","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32","country_code":"ES","type":"education","lineage":["https://openalex.org/I2802176441"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Roberto Castelli","raw_affiliation_strings":["BCAM -Basque Center for Applied Mathematics Bizkaia Technology Park, 48160 Derio, Bizkaia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BCAM -Basque Center for Applied Mathematics Bizkaia Technology Park, 48160 Derio, Bizkaia, Spain","institution_ids":["https://openalex.org/I2802176441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042598267","display_name":"Susanna Terracini","orcid":"https://orcid.org/0000-0002-6846-7841","observed_orcids":["https://orcid.org/0000-0002-6846-7841"]},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Susanna Terracini","raw_affiliation_strings":["Universit\u00e0 di Milano Bicocca , Dipartimento di Matematica e Applicazioni Via R. Cozzi 53 , 20125 Milano , Italy","University of Milan - Bicocca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Milano Bicocca , Dipartimento di Matematica e Applicazioni Via R. Cozzi 53 , 20125 Milano , Italy","institution_ids":["https://openalex.org/I66752286"]},{"raw_affiliation_string":"University of Milan - Bicocca","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0097,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.87283237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"30","issue":"4","first_page":"1197","last_page":"1218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7738999724388123,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7738999724388123,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.08030000329017639,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.024800000712275505,"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/regularization","display_name":"regularization","score":0.5649999976158142},{"id":"https://openalex.org/keywords/weak-singularity","display_name":"weak singularity","score":0.7739999890327454},{"id":"https://openalex.org/keywords/logarithmic-potential","display_name":"logarithmic potential","score":0.8830000162124634},{"id":"https://openalex.org/keywords/celestial-mechanics","display_name":"celestial mechanics","score":0.5690000057220459}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.807640552520752},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.7643616199493408},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.7567158937454224},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6977587342262268},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6818360090255737},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6352414488792419},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6095128059387207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45571163296699524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44788286089897156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3742435872554779},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3534072935581207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16904360055923462},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3934/dcds.2011.31.1197","doi":"https://doi.org/10.3934/dcds.2011.31.1197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/dcds.2011.31.1197","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=482741e0-602e-4ae0-ae75-d9ffbbf86015","source":{"id":"https://openalex.org/S19392275","display_name":"Discrete and Continuous Dynamical Systems","issn_l":"1078-0947","issn":["1078-0947","1553-5231"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Continuous Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:bird.bcamath.org:20.500.11824/627","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11824/627","pdf_url":null,"source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/bookPart"},{"id":"pmh:oai:arXiv.org:0905.1579","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.1579","pdf_url":"https://arxiv.org/pdf/0905.1579","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:iris.unito.it:2318/125662","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/125662","pdf_url":"http://arxiv.org/pdf/0905.1579","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research.vu.nl:openaire/710e4a8d-bdab-4a20-a4da-5a76491b3eec","doi":null,"is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/710e4a8d-bdab-4a20-a4da-5a76491b3eec","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,"listed_in":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Castelli, R & Terracini, S 2011, 'On the regularization of the collision solutions of the one-center problem with weak forces', Discrete and Continuous Dynamical Systems, vol. 31, no. 4, pp. 1197-1218. https://doi.org/10.3934/dcds.2011.31.1197","raw_type":"article"},{"id":"pmh:vu:oai:research.vu.nl:publications/710e4a8d-bdab-4a20-a4da-5a76491b3eec","doi":null,"is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/710e4a8d-bdab-4a20-a4da-5a76491b3eec","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Continuous Dynamical Systems, 31(4), 1197 - 1218. Southwest Missouri State University","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.0905.1579","doi":"https://doi.org/10.48550/arxiv.0905.1579","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0905.1579","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3934/dcds.2011.31.1197","doi":"https://doi.org/10.3934/dcds.2011.31.1197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/dcds.2011.31.1197","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=482741e0-602e-4ae0-ae75-d9ffbbf86015","source":{"id":"https://openalex.org/S19392275","display_name":"Discrete and Continuous Dynamical Systems","issn_l":"1078-0947","issn":["1078-0947","1553-5231"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Continuous Dynamical Systems","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/W2963230478.pdf","grobid_xml":"https://content.openalex.org/works/W2963230478.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1493815990","https://openalex.org/W1524565983","https://openalex.org/W1662316386","https://openalex.org/W1994986960","https://openalex.org/W2007726006","https://openalex.org/W2010264200","https://openalex.org/W2018017985","https://openalex.org/W2021496542","https://openalex.org/W2030573075","https://openalex.org/W2041858715","https://openalex.org/W2068771510","https://openalex.org/W2070037575","https://openalex.org/W2074527124","https://openalex.org/W2088842637","https://openalex.org/W2119347884","https://openalex.org/W2162416865","https://openalex.org/W2321164236","https://openalex.org/W2323511389","https://openalex.org/W2996339364","https://openalex.org/W3098925088","https://openalex.org/W3100870858","https://openalex.org/W4235146026","https://openalex.org/W7074652450"],"related_works":["https://openalex.org/W7047424836","https://openalex.org/W4362708131","https://openalex.org/W2804375585","https://openalex.org/W1965262321","https://openalex.org/W4246798914","https://openalex.org/W1672423924","https://openalex.org/W2156776491","https://openalex.org/W2105647700","https://openalex.org/W6996110931","https://openalex.org/W2065152881"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,17,24,31,39,58],"possible":[3],"regularization":[4,27],"of":[5,19,26,30],"collision":[6,43],"solutions":[7,44],"for":[8],"one":[9],"centre":[10],"problems":[11],"with":[12,47,55],"a":[13],"weak":[14],"singularity.":[15],"In":[16],"case":[18],"logarithmic":[20],"singularities,":[21],"we":[22,36],"consider":[23],"method":[25],"via":[28],"smoothing":[29],"potential.":[32],"With":[33],"this":[34],"technique,":[35],"prove":[37],"that":[38],"extended":[40],"flow,":[41],"where":[42],"are":[45],"replaced":[46],"transmission":[48],"trajectories,":[49],"is":[50],"continuous,":[51],"though":[52],"not":[53],"differentiable,":[54],"respect":[56],"to":[57],"initial":[59],"data.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-07-30T00:00:00"}
