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DC Field | Value | Language |
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dc.contributor.advisor | Vieiro Yanes, Arturo | - |
dc.contributor.author | Tellols Asensi, Oriol | - |
dc.date.accessioned | 2022-05-18T10:12:32Z | - |
dc.date.available | 2022-05-18T10:12:32Z | - |
dc.date.issued | 2021-06-20 | - |
dc.identifier.uri | http://hdl.handle.net/2445/185699 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Arturo Vieiro Yanes | ca |
dc.description.abstract | [en] In this work, we study the dynamics exhibited in 3 − dimensional parametric continuous dynamical systems containing a homoclinic orbit to a saddle-focus equilibrium. This setting gives rise to the Shilnikov bifurcation, which can be studied using an appropriate Poincaré section that reduces the original system into a discrete 2 − dimensional one. The bifurcation presents various cases, each showing rich and different dynamics. The Shilnikov Theorem describes one of the possible scenarios. This case follows from a careful analysis of a suitable return map that shows that dynamics in some regions is equivalent to the one of the horseshoe map. To illustrate properties and scenarios appearing at the bifurcation, we derive a family of systems with the desired properties and investigate them numerically. | ca |
dc.format.extent | 77 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Oriol Tellols Asensi, 2021 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Fluxos (Sistemes dinàmics diferenciables) | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Sistemes dinàmics diferenciables | ca |
dc.subject.classification | Sistemes dinàmics hiperbòlics | ca |
dc.subject.classification | Teoria de la bifurcació | ca |
dc.subject.other | Flows (Differentiable dynamical systems) | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Differentiable dynamical systems | en |
dc.subject.other | Hyperbolic dynamical systems | en |
dc.subject.other | Bifurcation theory | en |
dc.title | Richness of the dynamics at a Shilnikov bifurcation | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_tellols_asensi_oriol.pdf | Memòria | 3.91 MB | Adobe PDF | View/Open |
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