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The modern study of Differentiable Dynamical Systems began in the early sixties of this century. This began with the articles of M. Peixoto in 1959 and 1962, which deal with structural stability of 2-dimensional differential systems. The articles retreat the results announced by A. Andronov and L. Pontrjagin in 1937, extend them to closed surfaces, and add to them a new content concerning density properties. This attracted people's attention. It was mentioned in the introduction of his first article that "Therefore it seems natural to expect that a fruitful field of research lies in this direction". A natural question hence arisen: How about the case of dimensions higher than two? Since then, early or late, a number of mathematicians in the world, especially S. Smale, started their important research and probe on this topic.

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The modern study of Differentiable Dynamical Systems began in the early sixties of this century. This began with the articles of M. Peixoto in 1959 and 1962, which deal with structural stability of 2-dimensional differential systems. The articles retreat the results announced by A. Andronov and L. Pontrjagin in 1937, extend them to closed surfaces, and add to them a new content concerning density properties. This attracted people's attention. It was mentioned in the introduction of his first article that "Therefore it seems natural to expect that a fruitful field of research lies in this direction". A natural question hence arisen: How about the case of dimensions higher than two? Since then, early or late, a number of mathematicians in the world, especially S. Smale, started their important research and probe on this topic.