Perturbations o Lorenz-like flows.

• 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.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SMANIA, DANIEL; VIDARTE, JOSE. Existence of C-k-Invariant Foliations for Lorenz-Type Maps. Journal of Dynamics and Differential Equations, v. 30, n. 1, p. 227-255, MAR 2018. (09/17153-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

VIDARTE, Jose Humberto Bravo. Smooth pertubations of Lorenz-like flows. 2014. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.