Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2077286646', 'doi': 'https://doi.org/10.1007/bf00953662', 'title': 'The necessary conditions of the preservation of an invariant manifold of an autonomous system near an equilibrium point', 'display_name': 'The necessary conditions of the preservation of an invariant manifold of an autonomous system near an equilibrium point', 'publication_year': 1993, 'publication_date': '1993-05-01', 'ids': {'openalex': 'https://openalex.org/W2077286646', 'doi': 'https://doi.org/10.1007/bf00953662', 'mag': '2077286646'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf00953662', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S34928686', 'display_name': 'Zeitschrift für angewandte Mathematik und Physik', 'issn_l': '0044-2275', 'issn': ['0044-2275', '1420-9039'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5059104987', 'display_name': 'George Osipenko', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I212220629', 'display_name': 'Peter the Great St. Petersburg Polytechnic University', 'ror': 'https://ror.org/02x91aj62', 'country_code': 'RU', 'type': 'education', 'lineage': ['https://openalex.org/I212220629']}], 'countries': ['RU'], 'is_corresponding': False, 'raw_author_name': 'George Osipenko', 'raw_affiliation_strings': ['Dept of Mathematics, State Technical University, St. Petersburg,'], 'affiliations': [{'raw_affiliation_string': 'Dept of Mathematics, State Technical University, St. Petersburg,', 'institution_ids': ['https://openalex.org/I212220629']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5058665971', 'display_name': 'Eugene Ershov', 'orcid': None}, 'institutions': [], 'countries': ['RU'], 'is_corresponding': False, 'raw_author_name': 'Eugene Ershov', 'raw_affiliation_strings': ['Dept of Mathematics, Civil Engineering Institute, St. Petersburg, Russia'], 'affiliations': [{'raw_affiliation_string': 'Dept of Mathematics, Civil Engineering Institute, St. Petersburg, Russia', 'institution_ids': []}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2490, 'currency': 'EUR', 'value_usd': 3090, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 2, 'citation_normalized_percentile': {'value': 0.898506, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 61, 'max': 65}, 'biblio': {'volume': '44', 'issue': '3', 'first_page': '451', 'last_page': '468'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T14107', 'display_name': 'Social Sciences and Humanities Research', 'score': 0.9919, 'subfield': {'id': 'https://openalex.org/subfields/3300', 'display_name': 'General Social Sciences'}, 'field': {'id': 'https://openalex.org/fields/33', 'display_name': 'Social Sciences'}, 'domain': {'id': 'https://openalex.org/domains/2', 'display_name': 'Social Sciences'}}, 'topics': [{'id': 'https://openalex.org/T14107', 'display_name': 'Social Sciences and Humanities Research', 'score': 0.9919, 'subfield': {'id': 'https://openalex.org/subfields/3300', 'display_name': 'General Social Sciences'}, 'field': {'id': 'https://openalex.org/fields/33', 'display_name': 'Social Sciences'}, 'domain': {'id': 'https://openalex.org/domains/2', 'display_name': 'Social Sciences'}}, {'id': 'https://openalex.org/T12589', 'display_name': 'Nonlocal Partial Differential Equations and Boundary Value Problems', 'score': 0.9895, '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'}}, {'id': 'https://openalex.org/T10541', 'display_name': 'Theory and Applications of Fractional Differential Equations', 'score': 0.9657, '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/center-manifold', 'display_name': 'Center manifold', 'score': 0.7704442}, {'id': 'https://openalex.org/keywords/manifold', 'display_name': 'Manifold (fluid mechanics)', 'score': 0.636073}, {'id': 'https://openalex.org/keywords/equilibrium-point', 'display_name': 'Equilibrium point', 'score': 0.62893945}, {'id': 'https://openalex.org/keywords/stable-manifold', 'display_name': 'Stable manifold', 'score': 0.473725}, {'id': 'https://openalex.org/keywords/impulsive-differential-equations', 'display_name': 'Impulsive Differential Equations', 'score': 0.466277}], 'concepts': [{'id': 'https://openalex.org/C20483540', 'wikidata': 'https://www.wikidata.org/wiki/Q4200516', 'display_name': 'Invariant manifold', 'level': 2, 'score': 0.8615818}, {'id': 'https://openalex.org/C74774103', 'wikidata': 'https://www.wikidata.org/wiki/Q4504202', 'display_name': 'Center manifold', 'level': 5, 'score': 0.7704442}, {'id': 'https://openalex.org/C190470478', 'wikidata': 'https://www.wikidata.org/wiki/Q2370229', 'display_name': 'Invariant (physics)', 'level': 2, 'score': 0.7210992}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6466132}, {'id': 'https://openalex.org/C529865628', 'wikidata': 'https://www.wikidata.org/wiki/Q1790740', 'display_name': 'Manifold (fluid mechanics)', 'level': 2, 'score': 0.636073}, {'id': 'https://openalex.org/C94766913', 'wikidata': 'https://www.wikidata.org/wiki/Q1530271', 'display_name': 'Equilibrium point', 'level': 3, 'score': 0.62893945}, {'id': 'https://openalex.org/C51544822', 'wikidata': 'https://www.wikidata.org/wiki/Q465274', 'display_name': 'Ordinary differential equation', 'level': 3, 'score': 0.60476005}, {'id': 'https://openalex.org/C50429861', 'wikidata': 'https://www.wikidata.org/wiki/Q3554830', 'display_name': 'Stable manifold', 'level': 2, 'score': 0.473725}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.45123535}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.43597117}, {'id': 'https://openalex.org/C78045399', 'wikidata': 'https://www.wikidata.org/wiki/Q11214', 'display_name': 'Differential equation', 'level': 2, 'score': 0.41134202}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.12506711}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.10104862}, {'id': 'https://openalex.org/C2781349735', 'wikidata': 'https://www.wikidata.org/wiki/Q4904824', 'display_name': 'Bifurcation', 'level': 3, 'score': 0.06928724}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C172435161', 'wikidata': 'https://www.wikidata.org/wiki/Q531126', 'display_name': 'Hopf bifurcation', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C158622935', 'wikidata': 'https://www.wikidata.org/wiki/Q660848', 'display_name': 'Nonlinear system', 'level': 2, '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/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf00953662', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S34928686', 'display_name': 'Zeitschrift für angewandte Mathematik und Physik', 'issn_l': '0044-2275', 'issn': ['0044-2275', '1420-9039'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 9, 'referenced_works': ['https://openalex.org/W1887692392', 'https://openalex.org/W2027058059', 'https://openalex.org/W2073252807', 'https://openalex.org/W2742470390', 'https://openalex.org/W3141151088', 'https://openalex.org/W4230234443', 'https://openalex.org/W4233945890', 'https://openalex.org/W4239981491', 'https://openalex.org/W577424992'], 'related_works': ['https://openalex.org/W4236903077', 'https://openalex.org/W3152370143', 'https://openalex.org/W3021060928', 'https://openalex.org/W3013655172', 'https://openalex.org/W2243875171', 'https://openalex.org/W2129195111', 'https://openalex.org/W2087723889', 'https://openalex.org/W2041496883', 'https://openalex.org/W1983459863', 'https://openalex.org/W1536954903'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2077286646', 'counts_by_year': [{'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-08-15T08:25:16.729804', 'created_date': '2016-06-24'}