Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials
In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ones. We extend those results that contain some details related to differe...
- Autores:
-
Rodríguez Contreras, Contreras
Reyes Linero, Alberto
Campo Donado, Maria
Acosta-Humánez, Primitivo B.
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/6723
- Acceso en línea:
- https://hdl.handle.net/20.500.12442/6723
http://www.jsju.org/index.php/journal/article/view/674
- Palabra clave:
- Darboux first integral
Differential galois theory
Integrability
Orthogonal polynomial
Polynomials vector fields
达布第一积分
微分伽罗瓦理论
可积性
正交多项式
多项式矢量场
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| dc.title.translated.chi.fl_str_mv |
与正交多项式相关的平面多项式矢量场的动力学和代数分析 |
| title |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| spellingShingle |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials Darboux first integral Differential galois theory Integrability Orthogonal polynomial Polynomials vector fields 达布第一积分 微分伽罗瓦理论 可积性 正交多项式 多项式矢量场 |
| title_short |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| title_full |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| title_fullStr |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| title_full_unstemmed |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| title_sort |
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials |
| dc.creator.fl_str_mv |
Rodríguez Contreras, Contreras Reyes Linero, Alberto Campo Donado, Maria Acosta-Humánez, Primitivo B. |
| dc.contributor.author.none.fl_str_mv |
Rodríguez Contreras, Contreras Reyes Linero, Alberto Campo Donado, Maria Acosta-Humánez, Primitivo B. |
| dc.subject.eng.fl_str_mv |
Darboux first integral Differential galois theory Integrability Orthogonal polynomial Polynomials vector fields |
| topic |
Darboux first integral Differential galois theory Integrability Orthogonal polynomial Polynomials vector fields 达布第一积分 微分伽罗瓦理论 可积性 正交多项式 多项式矢量场 |
| dc.subject.chi.fl_str_mv |
达布第一积分 微分伽罗瓦理论 可积性 正交多项式 多项式矢量场 |
| description |
In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ones. We extend those results that contain some details related to differential Galois theory as well as the inclusion of Darboux theory of integrability and the qualitative theory of dynamical systems. We conclude this study with the construction of differential Galois groups, the calculation of Darboux first integral, and the construction of the global phase portraits |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2020-10-20T17:02:46Z |
| dc.date.available.none.fl_str_mv |
2020-10-20T17:02:46Z |
| dc.date.issued.none.fl_str_mv |
2020-08 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Artículo científico |
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02582724 |
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https://hdl.handle.net/20.500.12442/6723 |
| dc.identifier.doi.none.fl_str_mv |
10.35741/issn.0258-2724.55.4.29 |
| dc.identifier.url.none.fl_str_mv |
http://www.jsju.org/index.php/journal/article/view/674 |
| identifier_str_mv |
02582724 10.35741/issn.0258-2724.55.4.29 |
| url |
https://hdl.handle.net/20.500.12442/6723 http://www.jsju.org/index.php/journal/article/view/674 |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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http://purl.org/coar/access_right/c_abf2 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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pdf |
| dc.publisher.eng.fl_str_mv |
Southwest Jiaotong University |
| dc.source.eng.fl_str_mv |
JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY Vol. 55 No. 4, (2020) |
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Universidad Simón Bolívar |
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Rodríguez Contreras, Contrerasee7e3a60-ab5a-4924-a792-9305aa7c46bcReyes Linero, Albertof6c5a08e-d585-46b2-b0b7-0868117c3cb3Campo Donado, Maria1b399146-377e-4a5e-9ee4-5e74ea85dfe0Acosta-Humánez, Primitivo B.9439add6-3451-4b3f-b187-8b8ba4133fcd2020-10-20T17:02:46Z2020-10-20T17:02:46Z2020-0802582724https://hdl.handle.net/20.500.12442/672310.35741/issn.0258-2724.55.4.29http://www.jsju.org/index.php/journal/article/view/674In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ones. We extend those results that contain some details related to differential Galois theory as well as the inclusion of Darboux theory of integrability and the qualitative theory of dynamical systems. We conclude this study with the construction of differential Galois groups, the calculation of Darboux first integral, and the construction of the global phase portraits在当前的工作中，我们的目标是建立与正交多项式相关的二次多项式矢量场的一些族的研究 ，该正交多项式通过两种不同的观点相互关联，即定性和代数。 我们扩展了这些结果，这些结果 包含与微分加洛瓦理论有关的一些细节，以及包含达布可积性理论和动力学系统的定性理论。我 们以差分伽罗瓦群的构造，达布克斯第一积分的计算以及整体相像的构造来结束本研究。pdfengSouthwest Jiaotong UniversityAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITYVol. 55 No. 4, (2020)Darboux first integralDifferential galois theoryIntegrabilityOrthogonal polynomialPolynomials vector fields达布第一积分微分伽罗瓦理论可积性正交多项式多项式矢量场Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials与正交多项式相关的平面多项式矢量场的动力学和代数分析info:eu-repo/semantics/articleArtículo científicohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1ACOSTA-HUMÁNEZ, P.B., LÁZARO, J.T., MORALES-RUIZ, J.J., and PANTAZI, Ch. (2015) On the integrability of polynomial vector fields in the plane by means of PicardVessiot theory. Discrete and Continuous Dynamical Systems - Series A, 35, pp. 1767- 1800ACOSTA-HUMÁNEZ, P.B., DONADO, M.C., LINERO, A.R., and CONTRERAS, J.R. (2019) Algebraic and qualitative aspects of quadratic vector fields related with classical orthogonal polynomials. Available from https://arxiv.org/pdf/1906.09764.pdfDUMORTIER, F., LLIBRE, J., and ARTÉS, J.C. (2006) Qualitative Theory of Planar Differential Systems. Berlin, Heidelberg: SpringerGUCKENHEIMER, J., HOFFMAN, K., and WECKESSER, W. (2003) The forced Van der Pol equation I: The slowflow and its bifurcations. SIAM Journal on Applied Dynamical Systems, 2, pp. 1-35.KAPITANIAK, T. (1998) Chaos for Engineers: Theory, Applications and Control. Berlin: SpringerNAGUMO, J., ARIMOTO, S., and YOSHIZAWA, S. (1962) An active pulse transmission line simulating nerveaxon. Proceedings of the IRE, 50, pp. 2061-2070.PERKO, L. (2001) Differential Equations and Dynamical Systems. 3rd ed. New York: SpringerVAN DER POL, B. and VAN DER MARK, J. (1927) Frequency demultiplication. Nature, 120, pp. 363-364.ACOSTA-HUMÁNEZ, P., REYES, A., and RODRÍGUEZ, J. (2018) Galoisian and qualitative approaches to linear PolyaninZaitsev vector fields. Open Mathematics, 16, pp. 1204-1217.ACOSTA-HUMÁNEZ, P., REYES, A., and RODRÍGUEZ, J. (2018) Algebraic and qualitative remarks about the family yy′ = (αxm+k−1 + βxm−k−1)y + γx2m−2k−1 . Available from https://arxiv.org/pdf/1807.03551.pdf.ACOSTA-HUMANEZ, P.B. (2006) La Teoría de Morales-Ramis y el Algoritmo de Kovacic. Lecturas Matemáticas, 2, pp. 21- 56.ACOSTA-HUMÁNEZ, P. and PÉREZ, J.H. (2004) Una introducción a la Teoría de Galois diferencial. Boletín de Matemáticas, 11 (2), pp. 138-149RESPO, T. and HAJTO, Z. (2011) Algebraic Groups and Differential Galois Theory. Graduate Studies in Mathematics Series. Providence, Rhode Island: American Mathematical SocietyVAN DER PUT, M. and SINGER, M. (2003) Galois theory of linear differential equations. New York: Springer.LLIBRE, J. and XHANG, X. (2009) Darboux theory of integrability in Cn taking into account the multiplicity. Journal of Differential Equations, 246, pp. 541-551.ACOSTA-HUMÁNEZ, P.B., MORALES-RUIZ, J.J., and WEIL, J.-A. (2011) Galoisian approach to integrability of Schrödinger equation. Report on Mathematical Physics, 67, pp. 305-374.ACOSTA-HUMÁNEZ, P.B. and PANTAZI, Ch. (2012) Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations. Symmetry, Integrability and Geometry: Methods and Applications, 8, 043.CHIHARA, T.S. (1978) An Introduction to Orthogonal Polynomials. Mathematics and its Applications. New York: Gordon and Breach Science PublishersSMAIL, M.E.H. (2005) Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press.ACOSTA-HUMÁNEZ, P.B., LÁZARO, J.T., MORALES-RUIZ, J.J., and PANTAZI, Ch. (2018) Differential Galois theory and non-integrability of planar polynomial vector fields. Journal of Differential Equations, 264, pp. 7183-7212.MORALES-RUIZ, J.J. (1999) Differential Galois Theory and NonIntegrability of Hamiltonian Systems. Basel: Birkhäuser.MORALES-RUIZ, J.J. and RAMIS, J.- P. (2001) Galoisian obstructions to integrability of Hamiltonian systems. Methods and Applications of Analysis, 8, pp. 33-96.ACOSTA-HUMÁNEZ, P.B. (2010) Galoisian Approach to Supersymmetric Quantum Mechanics: The Integrability Analysis of the Schrödinger Equation by Means of Differential Galois Theory. Berlín: VDM Verlag, Dr. Müller.ACOSTA-HUMÁNEZ ， P.B. ， LÁZARO，J.T.，MORALES-RUIZ，J.J.， 和 PANTAZI，Ch。（2015）利用皮卡德· 维西奥特理论研究平面中多项式向量场的 可积性。离散和连续动力系统-系列一个 ，35，第 1767-1800 页。ACOSTA-HUMÁNEZ ， P.B. ， DONADO ， M.C. ， LINERO ， A.R. 和 CONTRERAS，J.R.（2019）与经典正交 多项式相关的二次矢量场的代数和质性方 面 。 可 从 https://arxiv.org/pdf/1906.09764.pdf 获得。DUMORTIER ， F. ， LLIBRE ， J. 和 ARTÉS，J.C. (2006) 平面微分系统的定性 理论。柏林，海德堡：施普林格。GUCKENHEIMER，J.，HOFFMAN， K. 和 WECKESSER，W.（2003）强迫范 德波尔方程 I：慢流及其分支。暹应用动 力系统杂志，2，第 1-35 页。KAPITANIAK，T.（1998）工程师的 混乱：理论，应用和控制。柏林：施普林 格。NAGUMO ， J. ， ARIMOTO ， S. 和 YOSHIZAWA，S.（1962）模拟神经轴突 的主动脉冲传输线。爱尔兰会议论文集， 50，第 2061-2070 页。PERKO，L.（2001）微分方程和动力 学系统。第三版。纽约：施普林格。 [8] B. VAN DER POL 和 J. VAN DER MARK（1927）频率解复用。自然，120 ，第 363-364 页。ACOSTA-HUMÁNEZ，P.，REYES， A. 和 RODRÍGUEZ，J.（2018）加洛瓦人 和定性方法研究线性聚多糖-扎伊采夫向 量场。开放式数学，16，第 1204-1217 页 。ACOSTA-HUMÁNEZ，P.，REYES， A., 和 RODRÍGUEZ，J.（2018）关于家庭 yy'=（αxm+ k-1 + βxm−k-1）y + γx2m−的 代数和定性 说 明 2k-1 。可从 https://arxiv.org/pdf/1807.03551.pdf 获取。ACOSTA-HUMANEZ，印刷。（2006 ）莫拉莱斯-拉米斯理论和科瓦维奇算法 ，2，第 21-56 页。P. ACOSTA-HUMÁNEZ 和 J.H. PÉREZ。（2004）发行了一份关于蒂罗亚 ·德·伽罗瓦（德卢瓦）的唱片。数学通讯 ，11（2），第 138-149 页。CRESPO，T. 和 HAJTO，Z.（2011） 代数群和微分伽罗瓦理论。数学研究生课 程系列。罗德岛州的普罗维登斯：美国数 学学会。VAN DER PUT，M。和 SINGER，M 。（2003）线性微分方程的加洛瓦理论。 纽约：施普林格。LLIBRE，J. 和 XHANG，X.（2009） 考虑到多重性，达布关于 Cn 可积性的理 论。微分方程学报，246，第 541-551 页。ACOSTA-HUMÁNEZ ， P.B. ， J.J 。 MORALES-RUIZ 和 J.-A. WEIL。（2011 ）薛定 ding 方程可积性的加洛瓦人方法。 数学物理，67，第 305-374 页。ACOSTA-HUMÁNEZ，铅。 和 潘塔 齐（2012）通过达布变换对薛定 er 平面向 量场进行达布积分。对称性，可积分性和 几何：方法与应用，8，043。千原，T.S.（1978）正交多项式简介 。数学及其应用。纽约：戈登和突破科学 出版社。ISMAIL，M.E.H。（2005）一变量中 的古典和量子正交多项式。数学及其应用 百科全书。剑桥：剑桥大学出版社。ACOSTA-HUMÁNEZ ， P.B. ， LÁZARO ， J.T. ， MORALES-RUIZ ， J.J. 和 PANTAZI，Ch。（2018）微分加洛瓦 理论和平面多项式矢量场的不可积性。微 分方程学报，264，第 7183-7212 页。MORALES-RUIZ，J.J。（1999）微 分伽罗瓦理论和哈密顿体系的非可积性。 巴塞尔：伯克豪斯。MORALES-RUIZ，J.J。和 RAMIS， J.-P.（2001）哈密尔顿系统对可积性的伽 罗瓦障碍。分析的方法和应用，8，第 33- 96 页。ACOSTA-HUMÁNEZ，铅。（2010） 超对称量子力学的伽罗瓦方法：借助微分 伽罗瓦理论对薛定 er 方程进行可积性分析 。贝琳：VDM 出版社，穆勒博士。ORIGINALPDF.pdfPDF.pdfPDFapplication/pdf1843938https://bonga.unisimon.edu.co/bitstreams/149bb1dd-1b6a-405a-a2fd-78fa5868d6b9/download3794afcd0faade15d704cb1c23b29a30MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://bonga.unisimon.edu.co/bitstreams/d7f17dda-b42c-4229-b155-e435aba23253/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-8381https://bonga.unisimon.edu.co/bitstreams/29fda109-ad8f-48a7-8755-7e2e2e92b867/download733bec43a0bf5ade4d97db708e29b185MD53TEXTDynamical and algebraic analysis of planar polynomial.pdf.txtDynamical and algebraic analysis of planar polynomial.pdf.txtExtracted texttext/plain37046https://bonga.unisimon.edu.co/bitstreams/d86e0794-32f1-4ed8-a94f-500451fb4dd6/download0de50003892eff3b7425358e69e8ec2dMD54PDF.pdf.txtPDF.pdf.txtExtracted texttext/plain38788https://bonga.unisimon.edu.co/bitstreams/d299f5d0-639e-45ff-bad5-f11c541b185c/download69bef438f9ff2dea963584a527eda0dcMD56THUMBNAILDynamical and algebraic analysis of planar polynomial.pdf.jpgDynamical and algebraic analysis of planar polynomial.pdf.jpgGenerated Thumbnailimage/jpeg1671https://bonga.unisimon.edu.co/bitstreams/bc476104-3213-4e1f-be59-2294e740c361/downloadc0460ae37b29c372dbb17994187d6f33MD55PDF.pdf.jpgPDF.pdf.jpgGenerated Thumbnailimage/jpeg5643https://bonga.unisimon.edu.co/bitstreams/42b1e7f4-3876-4858-9212-395c887ae379/download456e6e4411e77406f913b524eaa30de9MD5720.500.12442/6723oai:bonga.unisimon.edu.co:20.500.12442/67232024-08-14 21:53:21.1http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internacionalopen.accesshttps://bonga.unisimon.edu.coRepositorio Digital Universidad Simón Bolívarrepositorio.digital@unisimon.edu.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 |