Arithmetical signatures of the dynamics of the Hénon map

Detalhes bibliográficos
Autor(a) principal: Endler, Antônio
Data de Publicação: 2002
Outros Autores: Gallas, Jason Alfredo Carlson
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/101349
Resumo: We report a fourth-degree polynomial that parametrizes analytically all period-4 orbits of the Hénon map and use it to investigate arithmetical signatures of the symbolic coding for this prototypical multidimensional system. A discontinuity in the symbolic dynamics observed by Hansen while following numerically a period-6 orbit along a closed loop in parameter space is shown to exist already for period 4. We obtain an analytical expression for the locus of all such discontinuities in parameter space and explain their origin. Our analytical results allow the accurate location of all discontinuities, in contrast with topological methods based on homoclinic tangencies that exist over continuous intervals.
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spelling Endler, AntônioGallas, Jason Alfredo Carlson2014-08-19T02:10:22Z20021539-3755http://hdl.handle.net/10183/101349000314041We report a fourth-degree polynomial that parametrizes analytically all period-4 orbits of the Hénon map and use it to investigate arithmetical signatures of the symbolic coding for this prototypical multidimensional system. A discontinuity in the symbolic dynamics observed by Hansen while following numerically a period-6 orbit along a closed loop in parameter space is shown to exist already for period 4. We obtain an analytical expression for the locus of all such discontinuities in parameter space and explain their origin. Our analytical results allow the accurate location of all discontinuities, in contrast with topological methods based on homoclinic tangencies that exist over continuous intervals.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Vol. 65, no. 3 (Mar. 2002), 036231 11p.CaosMapeamento de HenonSistemas dinâmicos não-linearesTopologiaArithmetical signatures of the dynamics of the Hénon mapEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000314041.pdf000314041.pdfTexto completo (inglês)application/pdf369316http://www.lume.ufrgs.br/bitstream/10183/101349/1/000314041.pdf3cb938da92d3cadfc4f24d369b40bf73MD51TEXT000314041.pdf.txt000314041.pdf.txtExtracted Texttext/plain41452http://www.lume.ufrgs.br/bitstream/10183/101349/2/000314041.pdf.txtc3ea92bc0d6c687e381ecb8233cf7267MD52THUMBNAIL000314041.pdf.jpg000314041.pdf.jpgGenerated Thumbnailimage/jpeg1957http://www.lume.ufrgs.br/bitstream/10183/101349/3/000314041.pdf.jpg6e7981df192bca1e0b5e13b0a3dbf178MD5310183/1013492023-06-29 03:30:29.965432oai:www.lume.ufrgs.br:10183/101349Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-06-29T06:30:29Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Arithmetical signatures of the dynamics of the Hénon map
title Arithmetical signatures of the dynamics of the Hénon map
spellingShingle Arithmetical signatures of the dynamics of the Hénon map
Endler, Antônio
Caos
Mapeamento de Henon
Sistemas dinâmicos não-lineares
Topologia
title_short Arithmetical signatures of the dynamics of the Hénon map
title_full Arithmetical signatures of the dynamics of the Hénon map
title_fullStr Arithmetical signatures of the dynamics of the Hénon map
title_full_unstemmed Arithmetical signatures of the dynamics of the Hénon map
title_sort Arithmetical signatures of the dynamics of the Hénon map
author Endler, Antônio
author_facet Endler, Antônio
Gallas, Jason Alfredo Carlson
author_role author
author2 Gallas, Jason Alfredo Carlson
author2_role author
dc.contributor.author.fl_str_mv Endler, Antônio
Gallas, Jason Alfredo Carlson
dc.subject.por.fl_str_mv Caos
Mapeamento de Henon
Sistemas dinâmicos não-lineares
Topologia
topic Caos
Mapeamento de Henon
Sistemas dinâmicos não-lineares
Topologia
description We report a fourth-degree polynomial that parametrizes analytically all period-4 orbits of the Hénon map and use it to investigate arithmetical signatures of the symbolic coding for this prototypical multidimensional system. A discontinuity in the symbolic dynamics observed by Hansen while following numerically a period-6 orbit along a closed loop in parameter space is shown to exist already for period 4. We obtain an analytical expression for the locus of all such discontinuities in parameter space and explain their origin. Our analytical results allow the accurate location of all discontinuities, in contrast with topological methods based on homoclinic tangencies that exist over continuous intervals.
publishDate 2002
dc.date.issued.fl_str_mv 2002
dc.date.accessioned.fl_str_mv 2014-08-19T02:10:22Z
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dc.identifier.issn.pt_BR.fl_str_mv 1539-3755
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dc.relation.ispartof.pt_BR.fl_str_mv Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 65, no. 3 (Mar. 2002), 036231 11p.
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