# Deformations of one-dimensional dynamical systems

*Abstract:*

The goal of this mini-course is to give an introduction to the theory of deformations of one-dimensional dynamical systems.

A deformation of a dynamical system is a family of dynamical systems where the topological dynamics does not change. it is very easy to built deformations of structurally stable dynamical systems (expanding maps on the circle, Anosov diffeomorphisms), however the theory become far more interesting to more general dynamical systems (piecewise expanding maps, unimodal maps).

If we consider a deformation, it is natural to ask how the dynamically defined geometric properties of those maps changes with the parameter. We may consider periodic points, invariant measures, lyapunov exponents, etc. It is often the case that such geometric objects also moves smoothly with the parameter and we can calculate explicitly such derivatives.