Yorke, JA

Japanese: Yorke，J.A.（英語表記）YorkeJA

…For a = 4, if x _n is less than 1/2, set it as A , and if x _n > 1/2, set it as B , and an infinite sequence using the two symbols A and B is obtained. By moving the initial values appropriately, we can obtain exactly the same as the Bernoulli trial in terms of probability, that is, the infinite number of trials obtained by flipping a copper coin, where A is heads and B is tails. In 1975, mathematicians TY Li and JAY Orke proved that for a general one-dimensional interval dynamical system, if we consider the above repeated substitution x _{n +1} = f ( x _n ) (where f is continuous), if the sequence x _n has three periods, then any periodic solution can be obtained by changing the initial value, and that it has a solution that is not asymptotically periodic for uncountable initial values. They called this way of creating a sequence chaos. Chaos is a broader concept that includes randomness. …

*Some of the terminology references "Yorke, JA" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…a＝4では，x_nが1/2より小ならばAとおき，x_n＞1/2ならばBとおくと，二つのシンボルA,Bをつかった無限列が得られるが，初期値を適当に動かすことにより，確率でいうベルヌーイの試行，つまり銅貨投げで表ならばA，裏ならばBとして得られる無限回の試行とまったく同じものが得られる。数学者リーT.Y.LiとヨークJ.A.Yorkeは1975年，一般的な一次元区間力学系について，上の繰返し代入x_n＋1＝f(x_n)(ここでfは連続)を考えるなら，もし数列x_nが3周期をもてば，初期値をかえることによりどのような周期解ももちうること，および非可算の初期値に対し漸近的にも周期的でない解をもつことを証明し，このような数列のつくり方をカオスとよんだ。カオスはランダムを含むより広い概念である。…