Condition of chaos

1. Sep 30, 2011

mersecske

Usually positive Ljapunov exponent is said to be a condition for chaos,
and the strange atractor is so.

Are there any theorem which shows that the two condition is equivalent?
They are necessary and sufficent conditions?

2. Sep 30, 2011

Jack21222

The necessary conditions for chaos are topological mixing and sensitive dependence of initial conditions.

3. Jan 2, 2012

mersecske

Where can I find a precise statement and proof of "non-invertibility is necessary condition for chaos in 1D" ?