General terminology

Question 1

What is a map? What is a flow?

Answer 1

Map: discrete-time system, time proceeds in ‘clicks’

Flow: continuous-time system, time proceeds slowly

Question 2

Is a fractal state-space structure common in chaotic systems?

Answer 2

Yes

Question 3

What is a fixed point?

Answer 3

Topologically, they are where there is no flow.

Can be stable (flow is towards them) or unstable (flow is away from them).

Solved by equation f(x)=x, represents equilibrium point.

Question 4

What is a fixed point sink?

Answer 4

Sink attracts some epsilon neighborhood of nearby points, can be small or large.

Question 5

What does sensitive dependence on initial conditions mean?

Answer 5

That small variations in the initial conditions of the system can lead to widely divergent outcomes.

Question 6

What is a dynamical system?

Answer 6

A set of possible states with rules that determine the present state in terms of the past states. Must be deterministic.

Question 7

What is a Markov chain?

Answer 7

The future, if given the past, depends only on the present.