How typical is chaos?

Science / Mathematics

“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.

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