{"id":"https://openalex.org/W4239385295","doi":"https://doi.org/10.1007/978-3-319-58298-6_9","title":"The Adiabatic Invariance of the Action Variables","display_name":"The Adiabatic Invariance of the Action Variables","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W4239385295","doi":"https://doi.org/10.1007/978-3-319-58298-6_9"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-58298-6_9","doi":"https://doi.org/10.1007/978-3-319-58298-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-58298-6_9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463937","display_name":"Springer eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Classical and Quantum Dynamics","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4298350626","display_name":"Classical and Quantum Dynamics"},"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/A5111471185","display_name":"Walter Dittrich","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Walter Dittrich","raw_affiliation_strings":["Institute of Theoretical Physics, University of T\u00fcbingen, T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Physics, University of T\u00fcbingen, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":null,"display_name":"Martin Reuter","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Reuter","raw_affiliation_strings":["Institute of Physics, University of Mainz, Mainz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, University of Mainz, Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.48475967,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"119","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.2728999853134155,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.2728999853134155,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.1664000004529953,"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":0.10830000042915344,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adiabatic-invariance","display_name":"adiabatic invariance","score":1.0},{"id":"https://openalex.org/keywords/action-variables","display_name":"action variables","score":0.9980000257492065},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.6439999938011169},{"id":"https://openalex.org/keywords/action-angle-variables","display_name":"action-angle variables","score":0.5849999785423279},{"id":"https://openalex.org/keywords/elastic-collisions","display_name":"elastic collisions","score":0.48899999260902405}],"concepts":[{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.8845875859260559},{"id":"https://openalex.org/C133576831","wikidata":"https://www.wikidata.org/wiki/Q2632009","display_name":"Adiabatic invariant","level":3,"score":0.7688030004501343},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.6148871183395386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6012805700302124},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.599158525466919},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5443434715270996},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5131028890609741},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4624853730201721},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.43250831961631775},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.34867414832115173},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.295047402381897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2656306028366089},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17562612891197205},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07770523428916931},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-58298-6_9","doi":"https://doi.org/10.1007/978-3-319-58298-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-58298-6_9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463937","display_name":"Springer eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Classical and Quantum Dynamics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4403851130","https://openalex.org/W4242322376","https://openalex.org/W3013990856","https://openalex.org/W4251413171","https://openalex.org/W2049538331","https://openalex.org/W2062977329","https://openalex.org/W4232465102","https://openalex.org/W4285497633","https://openalex.org/W3217441148","https://openalex.org/W1998497446"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2022-05-12T00:00:00"}
