Computing the exact number of periodic orbits for planar flows
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2022 |
| Outros Autores: | |
| Tipo de documento: | Artigo |
| Idioma: | eng |
| Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
| Texto Completo: | http://hdl.handle.net/10400.1/17923 |
Resumo: | In this paper, we consider the problem of determining the exact number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits. |
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Computing the exact number of periodic orbits for planar flowsIn this paper, we consider the problem of determining the exact number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits.American Mathematical SocietySapientiaGraça, DanielZhong, Ning2022-07-07T12:27:55Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/17923eng1088-6850https://doi.org/10.1090/tran/8644info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:30:10Zoai:sapientia.ualg.pt:10400.1/17923Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:07:46.971485Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
| dc.title.none.fl_str_mv |
Computing the exact number of periodic orbits for planar flows |
| title |
Computing the exact number of periodic orbits for planar flows |
| spellingShingle |
Computing the exact number of periodic orbits for planar flows Graça, Daniel |
| title_short |
Computing the exact number of periodic orbits for planar flows |
| title_full |
Computing the exact number of periodic orbits for planar flows |
| title_fullStr |
Computing the exact number of periodic orbits for planar flows |
| title_full_unstemmed |
Computing the exact number of periodic orbits for planar flows |
| title_sort |
Computing the exact number of periodic orbits for planar flows |
| author |
Graça, Daniel |
| author_facet |
Graça, Daniel Zhong, Ning |
| author_role |
author |
| author2 |
Zhong, Ning |
| author2_role |
author |
| dc.contributor.none.fl_str_mv |
Sapientia |
| dc.contributor.author.fl_str_mv |
Graça, Daniel Zhong, Ning |
| description |
In this paper, we consider the problem of determining the exact number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits. |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022-07-07T12:27:55Z 2022 2022-01-01T00:00:00Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
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publishedVersion |
| dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.1/17923 |
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http://hdl.handle.net/10400.1/17923 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
1088-6850 https://doi.org/10.1090/tran/8644 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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American Mathematical Society |
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American Mathematical Society |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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