On page 26 he notes that Newton's laws of motion cannot predict the general result of three solid balls colliding simultaneously. At first I thought that this was not true since I remember solving problems like this in general physics. However, after further thought I realized that we can predict which direction a ball will be traveling after the collision only if we already know what happened to the other balls. In other words, we cannot predict the outcome of the collision entirely; we must know something about what happened.

**The above example may be considered as a subsequent loss of information that occurs following the collision of all three balls.**

Historically speaking, nonlinear systems subjected to analysis were either 1) treated only to first order where higher order effects were negligible (e.g. a simple pendulum displaced slightly from its resting position), or 2) too difficult to analyze thoroughly.

A system may appear periodic in a reduced-dimensional phase space (see Fig. 1.3). A corkscrew trajectory along one axis will appear circular when looking down this axis.

Period doubling leads to splitting in a system's power spectrum.

**As the number of period doublings occur, does the spectrum fill with peaks and appear as white noise (uniform power spectrum)? Does this form a link to diffusive processes?**(The Facebook link to white noise contains some block diagrams. Perhaps these can be shown to be equivalent to some chaotic systems.)

Chaos can emerge both in iterated function systems

*and*from sets of differential equations.

Chaotic systems may eventually settle into seemingly stable states and vice versa.