Mauricio Poletti
Mathematics
Although it is accessible compared to the famous phrase “butterfly effect”, engineer Mauricio Poletti’s objective is neither simple nor easy to understand: measuring the occurrence of chaos in dynamic systems—a fundamental investigation to expand knowledge about the unpredictability intrinsic to nature.
Mauricio was born in Paraguay and graduated in electrical engineering at the National University of Asunción. He directed his studies towards mathematics in his master’s and doctorate at the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro. The engineer also completed three postdoctoral periods. The first was at IMPA itself, the second at Université Paris 13, and finally, at Université Paris 11, France. He is currently a professor at the Federal University of Ceará.
Projects
“Flapping a butterfly’s wings in Brazil can cause a tornado in China.” Due to Lorenz’s works, this phrase is known as the butterfly effect. It says that small changes in a system’s initial conditions can produce significant changes in the long term; systems with this property are known as chaotic systems.
We study dynamic systems that evolve, represented by mathematical functions. My project aims to understand how often these systems exhibit chaotic behaviour. To do this, we measure chaos through two objects: the Lyapunov exponents and entropy. Thus, we want to understand what properties in systems imply that they have positive exponents and entropy, and in the space of all the systems we are studying (diffeomorphisms, endomorphisms, etc.), whether these conditions are typical.
