| Grant number: | 09/17153-9 |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| Start date: | April 01, 2010 |
| End date: | March 31, 2014 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Daniel Smania Brandão |
| Grantee: | Jose Humberto Bravo Vidarte |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
| Associated research grant: | 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems, AP.TEM |
Abstract Given a Lorenz-like flow X (either a geometric Lorenz flow or a flow similar to the so-called Rovella's attractor), we can associate to it an one-dimensional transformation f (defined on an interval). This allows us to study the dynamical properties for the original flow using techniques of one-dimensional dynamics. This association is called the reduction transformation $\mathcal{R}$. So we have RX=f. Since the most deep results in one-dimensional dynamics (as the phase-parameter relations in Jakobson's Theorem and renormalization theory) relays on the study of sufficiently smooth families of transformations, to transfer this result to Lorenz-like flows we need to study the smoothness of the reduction transformation R. There are already impressive results using this approach (in the particular case of Rovella s attractors, however if we had a more deep knowledge of the regularity of R then far more significative results could be achieved. In this project we will study the regularity of R and its consequences for the understanding of the dynamics of Lorenz-like flows. | |
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