Teorema de Takens, buenas observaciones y encajamientos casi-isométricos
In 1980, under the pretext of the turbulence phenomenon, Takens extends the weak Whitney embedding theorem such that an attractor, which in turn is a manifold, is topologically reconstructed from generic continuous dynamical system and experimental measurements of the object. This would revolutioniz...
- Autores:
-
Pérez Triana, Camilo Andrés
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/50824
- Acceso en línea:
- http://hdl.handle.net/1992/50824
- Palabra clave:
- Teorema de Takens
Sistemas dinámicos
Análisis de series de tiempo
Matemáticas
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
| Summary: | In 1980, under the pretext of the turbulence phenomenon, Takens extends the weak Whitney embedding theorem such that an attractor, which in turn is a manifold, is topologically reconstructed from generic continuous dynamical system and experimental measurements of the object. This would revolutionize part of the applicative mathematics, among them the time series and great application in various scientific disciplines such as physics, engineering or medicine. In the first part of the document, the original construction demonstration will be detailed, including some modern reformulations. In recent years there have been many efforts to improve this result, in particular two aspects: remove the idea of genericall property and making the reconstruction more accurate. As an approach to the first point, this work will deal with the good observations theorem, in the sense that if the dynamics of the system is fixed then it's possible to obtain conditions that determine whether or not a measurement... |
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