This is perhaps the paper that cemented his reputation as the "global master" of one-frequency cocycles. Avila proved that for a broad class of systems, "chaos" (positive Lyapunov exponents) is a dense phenomenon. This was a monumental shift in the understanding of how prevalent chaos truly is in deterministic systems.
A visit to Avila’s Google Scholar profile also offers a lesson in academic metadata. You may notice a small note: "Also known as: A. Avila, Artur Ávila" . Due to the inclusion of an accent on the 'A' (Ávila) in Portuguese, his papers are sometimes split into different profiles. artur avila google scholar
: Avila won a gold medal at the International Mathematical Olympiad at age 16 and completed his PhD at IMPA (Brazil) by age 21. This is perhaps the paper that cemented his
What stands out is not a single "hot topic" but a continuous thread: Avila moves fluidly between pure dynamical systems (how points move under repeated iterations of a map) and quantum physics (the spectrum of operators). A visit to Avila’s Google Scholar profile also
: Beyond the Fields Medal, he has received the Salem Prize (2006), the EMS Prize (2008), and the TWAS Prize (2013).
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