Rational limit cycles on generalized Bernouilli polynomial equations

Rational limit cycles on generalized Bernouilli polynomial equations

We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3. In particular, we show that when n = 3, there are equations with six rational limit cycles...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2021-03, Vol.62 (3)
1. Verfasser: Valls, Clàudia
Format: Artikel
Sprache:eng
Schlagworte:
Cycle ratio
Mathematical analysis
Physics
Polynomials
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 3
container_start_page
container_title Journal of mathematical physics
container_volume 62
creator Valls, Clàudia
description We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3. In particular, we show that when n = 3, there are equations with six rational limit cycles. We also show that the addressed problem can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then, we approach these equations by applying several tools; in particular, some developed to study extending Fermat problems for polynomial equations.
doi_str_mv 10.1063/5.0015230
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1063_5_0015230</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2494674966</sourcerecordid><originalsourceid>FETCH-LOGICAL-c327t-96b7cdb67032b9ed4832aa3a109be837f61246722cb27e655c4d5d4a9056bdb23</originalsourceid><addsrcrecordid>eNp90MtKAzEUBuAgCtbqwjcYcKUwNffLUusVCoLoOmQyGUlJJ9NkRqhP79iKLgRXZ_P9P-ccAE4RnCHIySWbQYgYJnAPTBCUqhScyX0wgRDjElMpD8FRzssRIUnpBNw8m97H1oQi-JXvC7uxweUitsWba10ywX-4urh2qY2DD8EXXQybNq78mHDrYRvOx-CgMSG7k-85Ba93ty_zh3LxdP84v1qUlmDRl4pXwtYVF5DgSrmaSoKNIQZBVTlJRMMRplxgbCssHGfM0prV1CjIeFVXmEzB2a63S3E9uNzrZRzSuHzWmKoxShXnozrfKZtizsk1ukt-ZdJGI6i_nqSZ_n7SaC92Nlvfb4_5we8x_ULd1c1_-G_zJ58IdOM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2494674966</pqid></control><display><type>article</type><title>Rational limit cycles on generalized Bernouilli polynomial equations</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Valls, Clàudia</creator><creatorcontrib>Valls, Clàudia</creatorcontrib><description>We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3. In particular, we show that when n = 3, there are equations with six rational limit cycles. We also show that the addressed problem can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then, we approach these equations by applying several tools; in particular, some developed to study extending Fermat problems for polynomial equations.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/5.0015230</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>New York: American Institute of Physics</publisher><subject>Cycle ratio ; Mathematical analysis ; Physics ; Polynomials</subject><ispartof>Journal of mathematical physics, 2021-03, Vol.62 (3)</ispartof><rights>Author(s)</rights><rights>2021 Author(s). Published under license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-96b7cdb67032b9ed4832aa3a109be837f61246722cb27e655c4d5d4a9056bdb23</citedby><cites>FETCH-LOGICAL-c327t-96b7cdb67032b9ed4832aa3a109be837f61246722cb27e655c4d5d4a9056bdb23</cites><orcidid>0000-0001-8279-1229</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/5.0015230$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,794,4512,27924,27925,76384</link.rule.ids></links><search><creatorcontrib>Valls, Clàudia</creatorcontrib><title>Rational limit cycles on generalized Bernouilli polynomial equations</title><title>Journal of mathematical physics</title><description>We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3. In particular, we show that when n = 3, there are equations with six rational limit cycles. We also show that the addressed problem can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then, we approach these equations by applying several tools; in particular, some developed to study extending Fermat problems for polynomial equations.</description><subject>Cycle ratio</subject><subject>Mathematical analysis</subject><subject>Physics</subject><subject>Polynomials</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp90MtKAzEUBuAgCtbqwjcYcKUwNffLUusVCoLoOmQyGUlJJ9NkRqhP79iKLgRXZ_P9P-ccAE4RnCHIySWbQYgYJnAPTBCUqhScyX0wgRDjElMpD8FRzssRIUnpBNw8m97H1oQi-JXvC7uxweUitsWba10ywX-4urh2qY2DD8EXXQybNq78mHDrYRvOx-CgMSG7k-85Ba93ty_zh3LxdP84v1qUlmDRl4pXwtYVF5DgSrmaSoKNIQZBVTlJRMMRplxgbCssHGfM0prV1CjIeFVXmEzB2a63S3E9uNzrZRzSuHzWmKoxShXnozrfKZtizsk1ukt-ZdJGI6i_nqSZ_n7SaC92Nlvfb4_5we8x_ULd1c1_-G_zJ58IdOM</recordid><startdate>20210301</startdate><enddate>20210301</enddate><creator>Valls, Clàudia</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-8279-1229</orcidid></search><sort><creationdate>20210301</creationdate><title>Rational limit cycles on generalized Bernouilli polynomial equations</title><author>Valls, Clàudia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-96b7cdb67032b9ed4832aa3a109be837f61246722cb27e655c4d5d4a9056bdb23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Cycle ratio</topic><topic>Mathematical analysis</topic><topic>Physics</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Valls, Clàudia</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Valls, Clàudia</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Rational limit cycles on generalized Bernouilli polynomial equations</atitle><jtitle>Journal of mathematical physics</jtitle><date>2021-03-01</date><risdate>2021</risdate><volume>62</volume><issue>3</issue><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3. In particular, we show that when n = 3, there are equations with six rational limit cycles. We also show that the addressed problem can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then, we approach these equations by applying several tools; in particular, some developed to study extending Fermat problems for polynomial equations.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0015230</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0001-8279-1229</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0022-2488
ispartof Journal of mathematical physics, 2021-03, Vol.62 (3)
issn 0022-2488
1089-7658
language eng
recordid cdi_crossref_primary_10_1063_5_0015230
source AIP Journals Complete; Alma/SFX Local Collection
subjects Cycle ratio
Mathematical analysis
Physics
Polynomials
title Rational limit cycles on generalized Bernouilli polynomial equations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T08%3A21%3A17IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Rational%20limit%20cycles%20on%20generalized%20Bernouilli%20polynomial%20equations&rft.jtitle=Journal%20of%20mathematical%20physics&rft.au=Valls,%20Cl%C3%A0udia&rft.date=2021-03-01&rft.volume=62&rft.issue=3&rft.issn=0022-2488&rft.eissn=1089-7658&rft.coden=JMAPAQ&rft_id=info:doi/10.1063/5.0015230&rft_dat=%3Cproquest_cross%3E2494674966%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2494674966&rft_id=info:pmid/&rfr_iscdi=true