Algebraic entropy: a primer

Claude-Michel Viallet (Sorbonne)

Tuesday 3rd March, 2020 16:00-17:00 Maths 311B


The starting point will be the simple question: given a discrete time dynamical system with an evolution given by a (bi)rational transformation, can we characterise its integrability or give measure how chaotic it is?
An answer is given by the algebraic entropy, which is a global index of complexity: its vanishing is the hallmark of integrability.
I will give the definition of the entropy and present a few of the ways to calculate it, as well as a challenging conjecture on the set of values it can take.

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