Dynamical Systems
نویسنده
چکیده
We think of this sequence as describing the time evolution of the point x. It will be convenient to denote the n-fold composition of f with itself by f, so f(x) is the result of n applications of f to x. In the theory of dynamical systems, we are typically interested in the long time behavior of orbits. This can depend very sensitively on small details, even in simple examples. As an illustration, consider the rotation by α on the unit circle S = {e : 0 ≤ φ < 2π}. So f(e) = e.
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