Invariantes E Equivariantes Relativos Para Grupos De Lie Compactos
A large variety of problems and models on bifurcation theory of dynamical systems have space symmetries and time reversing symmetries that are combined into a group of spacetime symmetries for the study of bifurcation theory of reversible-equivariant dynamical systems. One of the main methods of bif...
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| Format: | Master's thesis |
| Status: | Published version |
| Publication date: | 2017 |
| Country: | Brasil |
| Institution: | UNIFESP |
| Repository: | Repositório Institucional da UNIFESP |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.unifesp.br:11600/50648 |
| Online Access: | https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=5054531 https://repositorio.unifesp.br/handle/11600/50648 |
| Access Level: | Open access |
| Keyword: | Lie Groups And Lie Algebras Linear Representations Invariant Theory Organocatálise Reação Aldólica Síntese Assimétrica Sílicas Mesoporosas Ordenadas Sba-15 |
| Summary: | A large variety of problems and models on bifurcation theory of dynamical systems have space symmetries and time reversing symmetries that are combined into a group of spacetime symmetries for the study of bifurcation theory of reversible-equivariant dynamical systems. One of the main methods of bifurcation theory is to reduce to the normal form that attempt to simplify a vector field through coordinate transformations that preserve their local dynamical properties. In bifurcation theory of dynamical systems with symetries this is done with the aid of the theory of the invariants associated with the action of the spacetime symmetries group in question. In this dissertation, we present a unified theory of invariants under linear actions of compact Lie groups which generalizes the classical theory, including the reversing-time symetries, based on description of the srtucture of relativeinvariant polinomials and the structure of the relative-equivariant mappings. Finally, we discuss some computational aspects that are naturally motivated by the main results of the theory. |
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