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I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

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Chapter 14 3 1 1 13 14.1 (dynamical system) a n+1 = 2a n ; a 0 = 1. a n = 2 n f(x) = 2x a n+1 = f(a n ) a 1 = f(a 0 ), a 2 = f(f(a 0 )) a 3 = f(f(f(a 0 ))) f a 0 1 2 14 3 *1 {a n } R 0, ±1, ±2, x 1 f(x)

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II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

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2000年度『数学展望 I』講義録

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Jacobson Prime Avoidance

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1.3 1.4. (pp.14-27) 1 1 : f(z = re iθ ) = u(r, θ) + iv(r, θ). (re iθ ) 2 = r 2 e 2iθ = r 2 cos 2θ + ir 2 sin 2θ r f(z = x + iy) = u(x, y) + iv(x, y). (x + iy) 2 = x 2 y 2 + i2xy x = 1 y (1 + iy) 2 = 1

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