Probabilistic and algebraic aspects of smooth dynamical systems
Self-similarity and the transition from finite to infinite measures in dynamical s...
Differential equations: a dynamical approach for the Poincaré-Hopf Theorem
Grant number: | 16/21492-7 |
Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
Start date until: | March 01, 2017 |
End date until: | February 28, 2018 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics |
Principal Investigator: | Liane Bordignon |
Grantee: | Gabriel Longatto Clemente |
Host Institution: | Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil |
Abstract The aim of this project is to give the student an elemental background in one dimensional discrete dynamics systems, preparing him to research in this subject. It proposes the study of the first chapter of "An introduction to chaotic dynamical systems" of R. Devaney, complemented by more advanced texts addressed to researchers in the area, improving the scientific maturity of the student. The candidate will study fundamental concepts of dynamical systems, including symbolic dynamics, Devaney's chaos definition, Sarkovskii's Theorem, structural stability, dynamics in $S^1$ and fragments of kneading theory. At the end, the student will have seen a description of the very illustrative behaviour of the family $F_\mu(x)= \mu x(1-x)$, $\mu \in \mathbb{R}, \mu \geq 1$, including the period duplication phenomenon and the Poincaré Classification Theorem for $S^1$ homeomorphisms. (AU) | |
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