Artur Avila is a Brazilian mathematician who has contributed to a number of fields. Some of his most notable research is in the study of chaos theory and dynamical systems. These areas seek to understand the behavior of systems that evolve over time in which very small changes in initial conditions can lead to wildly varying outcomes, such as weather patterns, as typified in the classic example of a butterfly's wings flapping leading to a change in weather hundreds of miles away.
One of Avila's major contributions to this field of study was in clarifying that a certain broad class of dynamical systems fall into one of two categories. They either eventually evolve into a stable state, or fall into a chaotic stochastic state, in which their behavior can be described probabilistically.
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