Condesned knowledge from scientific papers

This section focus on chaos theory

Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiard

Billiard ball collisions are convex, thus the only souce causing hyberbolic instability is defocusing.

For each conservation law in the system - there will be a pair of Lyapunov exponets corresponing to the conserved quantites that are zero.

Calculation of Lyapunov exponents for dynamic systems with discontinuities

The sum of the Lyapunov exponents is the average volume contraction rate (of a ball of inital points in phase space).

There is a systamatic way (shown in this paper) of solving the Lyapunov exponents for hard impacts and sliding frictions (problematic as the points move discontinusouly through phase space).