Finding invariant tori in the problem of a periodically corrugated waveguide
Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.
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| Format: | Digital revista |
| Langue: | English |
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Sociedade Brasileira de Física
2008
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oai:scielo:S0103-973320080001000102008-03-27Finding invariant tori in the problem of a periodically corrugated waveguideRabelo,Adriano FábioLeonel,Edson D. Chaos Invariant Spanning Curves Nonlinear Mappings Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.info:eu-repo/semantics/openAccessSociedade Brasileira de FísicaBrazilian Journal of Physics v.38 n.1 20082008-03-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332008000100010en10.1590/S0103-97332008000100010 |
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BR |
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revista |
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America del Sur |
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| language |
English |
| format |
Digital |
| author |
Rabelo,Adriano Fábio Leonel,Edson D. |
| spellingShingle |
Rabelo,Adriano Fábio Leonel,Edson D. Finding invariant tori in the problem of a periodically corrugated waveguide |
| author_facet |
Rabelo,Adriano Fábio Leonel,Edson D. |
| author_sort |
Rabelo,Adriano Fábio |
| title |
Finding invariant tori in the problem of a periodically corrugated waveguide |
| title_short |
Finding invariant tori in the problem of a periodically corrugated waveguide |
| title_full |
Finding invariant tori in the problem of a periodically corrugated waveguide |
| title_fullStr |
Finding invariant tori in the problem of a periodically corrugated waveguide |
| title_full_unstemmed |
Finding invariant tori in the problem of a periodically corrugated waveguide |
| title_sort |
finding invariant tori in the problem of a periodically corrugated waveguide |
| description |
Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter. |
| publisher |
Sociedade Brasileira de Física |
| publishDate |
2008 |
| url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332008000100010 |
| work_keys_str_mv |
AT rabeloadrianofabio findinginvarianttoriintheproblemofaperiodicallycorrugatedwaveguide AT leoneledsond findinginvarianttoriintheproblemofaperiodicallycorrugatedwaveguide |
| _version_ |
1756407439215820800 |