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| Author(s): |
Felipe Emanoel Chaves
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2013-12-17 |
| Examining board members: |
Marco Antonio Teixeira;
Ricardo Miranda Martins;
Claudio Aguinaldo Buzzi;
Luiz Fernando de Osório Mello;
Regilene Delazari dos Santos Oliveira
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| Advisor: | Marco Antonio Teixeira |
| Abstract | |
In this work we'll discuss some qualitative/geometric aspects of non-smooth dynamical systems with symmetry. Our goal is to develop a systematic method for the study of local (and global) bifurcation in two classes of non-smooth dynamic systems with symmetry, called reversible Filippov systems and equivariant Filippov systems. The concepts of reversibility and equivariance are linked to a given involution. For a large class of Filippov planar reversible fields and Filippov planar equivariant fields, where, locally, the set of fixed points of the involution is equal to the discontinuity variety of the Filippov field, we present all topological types and normal forms of codimension 0 and 1 singularities, as well as all their respective bifurcation diagrams. Beyond that, we present all topological types and normal forms of codimension 2 singularities for the reversible Filippov fields to this involution, sketching some of their bifurcation diagrams. We also discuss, in these cases, the existing relations between the reversible Filippov fields and the reversible smooth fields. At the end, we propose a classification for the codimension 0 and 1 singularities of the Filippov reversible or equivariant fields, for the case where the dimension of the set of the fixed points of the given involution is zero, finalizing with some proposals for future work (AU) | |
| FAPESP's process: | 09/08946-5 - Symmetries and Discontinuous Systems |
| Grantee: | Felipe Emanoel Chaves |
| Support Opportunities: | Scholarships in Brazil - Doctorate |