Interesting facts: Flow
The motion of a point on a surface is described by what mathematicians call a flow, i.e. a collection of transformations ft parametrized by time t, where ft is the transformation that tells where each point gets to in time t
An important feature of flows, which arise from billiards and the Novikov model, is that they are incompressible and area-preserving, i.e. the area of a set does not change over time.
This property allows mathematicians to study these flows using the tools of a branch of mathematics known as ergodic theory, which stems from the work in the 1930s of the physicist Boltzmann and mathematicians Neumann and Birkhoff.
