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- くにひと あいしま
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1 Tel : , Fax : tohru@ics.saitama-u.ac.jp URL : tohru / / p.1/12
2 / / p.2/12
3 1 0.8 x(t) t / / p.2/12
4 1 0.8 x(t) t / / p.2/12
5 1 0.8 x(t) t / / p.2/12
6 1 0.8 x(t) t / / p.2/12
7 1 0.8 x(t) t / / p.2/12
8 1 0.8 x(t) t / / p.2/12
9 1 0.8 x(t) t / / p.2/12
10 Power Frequency / / p.3/12
11 x(t) x(3) (x(3), x(4)) (x(2), x(3)) x(2) x(1) (x(1), x(2)) t / / p.4/12
12 ! x(t+1) x(t) / / p.5/12
13 1 0.8 x(t) ( ). x(t + 1) = 4x(t)(1 x(t)) (logistic map) t / / p.6/12
14 x(t + 1) = 4x(t)(1 x(t)) t = 0 x(0)( ) x(1) t = 1 x(1) x(2) / / p.7/12
15 / / p.8/12
16 / / p.8/12
17 1. 1 x(t + 1) = 4x(t)(1 x(t)) / / p.8/12
18 x(t) x(t + 1) x(t + 1) = 4x(t)(1 x(t)) / / p.8/12
19 x(t) x(t + 1) 3. 2 x(t + 1) = 4x(t)(1 x(t)) / / p.8/12
20 / / p.9/12
21 2 (17c) 3 (19c) / / p.9/12
22 2 (17c) 3 (19c) 1. / / p.9/12
23 2 (17c) 3 (19c) / / p.9/12
24 2 (17c) 3 (19c) / / p.9/12
25 2 (17c) 3 (19c) / / p.9/12
26 2 (17c) 3 (19c) / / p.9/12
27 2 (17c) 3 (19c) / / p.9/12
28 2 (17c) 3 (19c) (a) (b) 2 / / p.9/12
29 2 (17c) 3 (19c) (a) (b) / / p.9/12
30 / / p.10/12
31 1. Henri Poincaré 3 / / p.10/12
32 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) / / p.10/12
33 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) 3. J. von Neumann, S. M. Ulam (1947) On combination of stochastic and deterministic process, f (x) = 4x(1 x) / / p.10/12
34 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) 3. J. von Neumann, S. M. Ulam (1947) On combination of stochastic and deterministic process, f (x) = 4x(1 x) 4. R. E. Kalman (1956) / / p.10/12
35 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) 3. J. von Neumann, S. M. Ulam (1947) On combination of stochastic and deterministic process, f (x) = 4x(1 x) 4. R. E. Kalman (1956) 5. Y. Ueda, H. Kawakami, N. Akamatsu (1960 s) / / p.10/12
36 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) 3. J. von Neumann, S. M. Ulam (1947) On combination of stochastic and deterministic process, f (x) = 4x(1 x) 4. R. E. Kalman (1956) 5. Y. Ueda, H. Kawakami, N. Akamatsu (1960 s) 6. E. N. Lorenz (1963) / / p.10/12
37 1. Henri Poincaré 3 2. van der Pol, van der Mark (1927) 3. J. von Neumann, S. M. Ulam (1947) On combination of stochastic and deterministic process, f (x) = 4x(1 x) 4. R. E. Kalman (1956) 5. Y. Ueda, H. Kawakami, N. Akamatsu (1960 s) 6. E. N. Lorenz (1963) 7. T. Y. Li & J. A. Yorke (1975),Period Three Implies Chaos / / p.10/12
38 ( ) : (2001) / / p.11/12
39 URL : tohru/lectures/ / / p.12/12
(a) (b) (c) 4. (a) (b) (c) p.2/27
338 8570 255 Tel : 048 858 3577 Fax : 048 858 3716 Email : tohru@ics.saitama-u.ac.jp URL : http://www.nls.ics.saitama-u.ac.jp/ tohru Copyright (C) 2002, Tohru Ikeguchi, Saitama University. All rights reserved.
(time series) ( 225 ) / / p.2/66
338 857 255 Tel : 48 858 3577, Fax : 48 858 3716 Email : tohru@ics.saitama-u.ac.jp URL : http://www.nls.ics.saitama-u.ac.jp/ tohru / / p.1/66 (time series) ( 225 ) / / p.2/66 / / p.3/66 ?? / / p.3/66 1.9.8.7.6???.5.4.3.2.1
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On Applications of Rigorous Computing to Dynamical Systems (Zin ARAI) Department of Mathematics, Kyoto University email: arai@math.kyoto-u.ac.jp 1 [12, 13] Lorenz 2 Lorenz 3 4 2 Lorenz 2.1 Lorenz E. Lorenz