DIRECTIONS IN CLASSICAL CHAOS

Though not yet widely recognized, chaos theory now illuminates four highly significant problems in the foundations of classical dynamics. Specifically, the notions of chaos may lead to verification of the following conjectures:

1. The existence of a generalized uncertainty principle which asserts that no physical variable can be measured precisely.

2. The use of chaos to solve problems which heretofore either have not been or cannot be solved deterministically.

3. The expansion of the notion of integrability to include all systems which are ergodic (only) or mixing (only).

4. The use of judiciously chosen integrable, nearly integrable, or algorithmically integrable many-body systems to control chaos.