The Bernoulli shift as a basic chaotic dynamical system

Abstract

We give a brief introduction to the Bernoulli shift map as a basic chaotic dynamical system. We give several examples where the iterates of a mapping can be understood using the Bernoulli shift.

Namely, the iteration of real interval maps and iteration of quadratic functions in the complex plain.

Keywords

• Bernoulli shift
• chaotic dynamics
• recurrence