Dynamical systems is a branch of mathematics which studies processes which change.
Such processes occur in all branches of science, and examples of dynamical systems include the motion of stars, the change of stock markets, the variation of the world's weather, the rise and fall of populations, the reaction of chemicals and the motion of a simple pendulum. The study of dynamical systems originated from differential or difference equations arising from many applied fields, and has been one of the most fruitful fields of mathematical research in this century. Many profound results have been uncovered and applied to other branches of mathematics as well as to physics, chemistry, biology and economics. In this course, we will use maps in low-dimensional Euclidean spaces to demonstrate the main contents, methods and applications of dynamical systems. The course will be structured so that students are gradually introduced to more and more sophisticated ideas from analysis as the course proceeds.