Exterior discrete semi-flows

An exterior discrete semi-flow is a discrete semi-flow generated by an exterior continuous map. The aim of this doctoral thesis is to profoundly study the notion of exterior discrete semi-flow and to apply it to the analysis of iterative processes induced by some numerical methods. Firstly, we estab...

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Autor principal:	Marañon Grandes, Miguel
Otros Autores:	Hernández Paricio, Luis Javier (Universidad de La Rioja)
Formato:	text (thesis)
Lenguaje:	eng
Publicado:	Universidad de La Rioja (España) 2015
Acceso en línea:	https://dialnet.unirioja.es/servlet/oaites?codigo=46123
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spelling	oai-TES00000086942019-07-14Exterior discrete semi-flowsMarañon Grandes, MiguelAn exterior discrete semi-flow is a discrete semi-flow generated by an exterior continuous map. The aim of this doctoral thesis is to profoundly study the notion of exterior discrete semi-flow and to apply it to the analysis of iterative processes induced by some numerical methods. Firstly, we establish connections in dimension 0 among three of the most usual end sets of an exterior space and their analogues in the category of exterior discrete semi-flows: those of Brown-Grossman, Steenrod and Borsuk-Cech. After that, with a view to make a study about basins of attraction of fixed and, in general, m-periodic points associated with a rational map defined on the surface of the sphere S2, we consider externologies given by families of the open subsets that contain determined right-invariant subsets; in this way, we are connecting some novel working purely topological techniques to several notions regarding discrete semi-flows and dynamical systems. Next, in order to set a theoretical framework in which the algorithms that have been designed and implemented along this work make sense, we focus on the development of the study of discrete semi-flows on metric spaces and on the creation of a new procedure to introduce measures on CW-complexes which allow us to estimate in a computational manner and compare the sizes of basins of end points. With this, we are building a bridge between the topological and the computational part of this thesis. Finally, relying on the theorems proved and on the geometry and the complex structure of the Riemann sphere, we present new computer programs written in Sage and Mathematica for visualizing the basins of attraction associated with the end points of a discrete semi-flow induced by a rational function different from the identity defined on the surface of the sphere S2 and for computing the measure of these basins of attraction, up to a certain precision.Universidad de La Rioja (España)Hernández Paricio, Luis Javier (Universidad de La Rioja)Rivas Rodríguez, María Teresa (Universidad de La Rioja)2015text (thesis)application/pdfhttps://dialnet.unirioja.es/servlet/oaites?codigo=46123engLICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI \| INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI
institution	DialNet
collection	DialNet
language	eng
description	An exterior discrete semi-flow is a discrete semi-flow generated by an exterior continuous map. The aim of this doctoral thesis is to profoundly study the notion of exterior discrete semi-flow and to apply it to the analysis of iterative processes induced by some numerical methods. Firstly, we establish connections in dimension 0 among three of the most usual end sets of an exterior space and their analogues in the category of exterior discrete semi-flows: those of Brown-Grossman, Steenrod and Borsuk-Cech. After that, with a view to make a study about basins of attraction of fixed and, in general, m-periodic points associated with a rational map defined on the surface of the sphere S2, we consider externologies given by families of the open subsets that contain determined right-invariant subsets; in this way, we are connecting some novel working purely topological techniques to several notions regarding discrete semi-flows and dynamical systems. Next, in order to set a theoretical framework in which the algorithms that have been designed and implemented along this work make sense, we focus on the development of the study of discrete semi-flows on metric spaces and on the creation of a new procedure to introduce measures on CW-complexes which allow us to estimate in a computational manner and compare the sizes of basins of end points. With this, we are building a bridge between the topological and the computational part of this thesis. Finally, relying on the theorems proved and on the geometry and the complex structure of the Riemann sphere, we present new computer programs written in Sage and Mathematica for visualizing the basins of attraction associated with the end points of a discrete semi-flow induced by a rational function different from the identity defined on the surface of the sphere S2 and for computing the measure of these basins of attraction, up to a certain precision.
author2	Hernández Paricio, Luis Javier (Universidad de La Rioja)
author_facet	Hernández Paricio, Luis Javier (Universidad de La Rioja) Marañon Grandes, Miguel
format	text (thesis)
author	Marañon Grandes, Miguel
spellingShingle	Marañon Grandes, Miguel Exterior discrete semi-flows
author_sort	Marañon Grandes, Miguel
title	Exterior discrete semi-flows
title_short	Exterior discrete semi-flows
title_full	Exterior discrete semi-flows
title_fullStr	Exterior discrete semi-flows
title_full_unstemmed	Exterior discrete semi-flows
title_sort	exterior discrete semi-flows
publisher	Universidad de La Rioja (España)
publishDate	2015
url	https://dialnet.unirioja.es/servlet/oaites?codigo=46123
work_keys_str_mv	AT maranongrandesmiguel exteriordiscretesemiflows
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Exterior discrete semi-flows

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