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6. On the co-existence of chaos and applied mathematics

The appearance of Chaos in simple non-linear systems is quite disturbing from an applied mathematician point of view; For example, if the deterministic model leads to chaos what can be predicted regarding the solutions? How can different models be distinguished, and thus, can we determine which one correctly describes the system at hand? How can we distinguish between chaotic systems and systems with noise? These naive, application oriented questions, lead naturally to fundamental concepts in dynamical systems such as structural stability, normal forms, bifurcation theory and the study of limiting sets. Furthermore, attempts to address these issues immediately lead to problematic questions regarding transients vs. limiting behaviors in various systems. While one cannot address all these issues in a lifetime, I will discuss how some of them arise and are partially resolved in a few applications.

Michael Grinfeld 2002-10-23