In this review, some of the fundamental concepts of the theory of classical chaos are presented in a pedagogical style. The paper is directed primarily to readers without any prerequisite knowledge of the subject matter apart from a good background orientation in undergraduate mathematics. Our approach is to a large extent geometrical and is motivated by specific problems of physical interest and illustrated by examples. Neither the notion of "quantum chaos", nor the probabilistic aspects of chaos requiring certain familiarity with statistical physics are treated here. In particular, the following questions are addressed: (a) What are the fundamental scientific issues that the science of chaos aims to resolve? (b) What are the main new ideas and methods that chaos puts forward to achieve these goals? (c) How successful has chaos been so far in providing solutions to concrete problems?
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics