諃崭謧斩斋战斋 11-斋斩諠 摘铡沾炸 13謮00-斋斩, 缘諍諃 沾铡诈榨沾铡湛斋寨铡盏斋 謬 沾榨窄铡斩斋寨铡盏斋 謫铡寨崭謧宅湛榨湛斋 137 宅战铡謤铡斩崭謧沾 寨铡斩謥寨铡謥站斋 芦Dynamics, Chaos, and Fractals禄 诈榨沾铡盏崭站 眨斋湛铡寨铡斩 战榨沾斋斩铡謤炸:
远榨寨崭謧盏謥崭站 瞻铡斩栅榨战 寨眨铡 员談諉 钥铡斩咋铡战 斩铡瞻铡斩眨斋 瞻铡沾铡宅战铡謤铡斩斋 (Kansas State University, USA) 蘸謤崭謫榨战崭謤 諃謤铡斩湛 諃铡寨崭闸盏铡斩炸謮
諐榨沾斋斩铡謤斋 诈榨沾铡斩 謬 斩寨铡謤铡眨謤崭謧诈盏崭謧斩炸
Given a function f:\mathbb{R}\to\mathbb{R} and a point x=x_0\in\mathbb{R} the orbit of x under f is the sequence x_n =f^{\circ n}(x_0), where f^{\circ n} denotes the n-th iterate of f, that is f^{\circ n}=f\circ \ldots \circ f. When fis a linear function then every orbit of every point can be easily described completely.
However, even for the easiest non-linear functions of the form f(x)=x^2+c the situation becomes completely different and description of orbits becomes much more difficult and even impossible.
Nevertheless, it turns out that qualitative behavior of most orbits for most quadratic functions is indeed possible.
Understanding this leads one to the notion of chaos, unpredictability, fractals, and many other interesting concepts which we will describe in this lecture.