Dynamical systems are a notoriously difficult field of mathematics to which Henri Poincaré (1854–1912) made major contributions (see Tangente SUP 67-68, 2013). Yet the field features a horseshoe, "tamed" by Stephen Smale on the beaches of Copacabana in Rio de Janeiro (see Tangente 128, 2009). This object consists of a sequence of very simple geometric operations (the baker's map) applied to a surface: contraction in one dimension, stretching in another, and folding into the shape of... a horseshoe.
Much like this horseshoe, which gives rise to "chaotic" behavior, the Anosov flow results from expanding a surface in one direction, contracting it along others, and repeating these operations. The mathematician Dmitri Viktorovich Anosov (1936–2014) studied this object extensively.
The image by artist Jos Leys (**www.josleys.com**) featured on the cover depicts a surface (in green) and the unstable orbit associated with an Anosov flow defined on that surface. An abstract mathematical trajectory, in short!
