## Flat Surfaces, Frontiers in Number Theory

- Zorich, Anton
- Physics and Geometry,
- 2006

The local behaviour of a dynamical system on a manifold M given by the iterations of a di erentiable map T : M →M can be investigated by studying its di erential. Under the Jacobian DT (x), a small sphere centred at a point x ∈M is, approximately, mapped to an ellipsoid centred at Tx. Subsequent applications of the derivative along the orbit of x stretch… (More)