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 A320480 a(n) = floor(x(n)), where (x(n),y(n)) are defined by the Chirikov "standard map" y(n) = y(n-1)+3*sin(x(n-1)), x(n) = x(n-1)+y(n), with x(0)=y(0)=1. 6
 1, 4, 5, 2, 1, 2, 5, 4, 1, 0, 0, 0, 2, 6, 10, 12, 12, 11, 7, 7, 9, 10, 9, 8, 9, 10, 8, 9, 10, 9, 7, 8, 11, 11, 8, 7, 10, 10, 8, 8, 11, 10, 7, 6, 6, 5, 1, 1, 3, 4, 2, 2, 4, 4, 0, 0, 1, 5, 6, 8, 12, 18, 21, 26, 34, 42, 46, 52, 59, 67, 71, 77, 86, 91, 95, 103, 111, 116, 120, 127, 137, 144, 153, 163, 172, 182, 195, 210, 225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The Chirikov map is an example of a nonlinear dynamical system which can exhibit chaotic behavior. Most such maps do not easily lead to integer sequences, but this map does. Note that some websites reduce x(n) mod 2*Pi, but this version does not. More than the usual number of terms are shown in order to reach an interesting region of terms. REFERENCES H. A. Lauwerier, Two-dimensional iterative maps, Chapter 4 of A. V. Holden, ed., Chaos, Princeton, 1986. See Eq. (4.67). E. N. Lorenz, The Essence of Chaos, Univ. Washington Press, 1993. See p 191. LINKS Roderick V. Jensen, Classical chaos, American Scientist 75.2 (1987): 168-181. See Eq. (2), (3). EXAMPLE The initial values of x(n) and y(n) are 1, 4.524412954, 5.101672501, 2.903388389, 1.412978211, 2.885285674, 5.118122864, 4.594521097, 1.091734472, 0.251231092, 0.1565174874, 0.5294415308, 2.417519808, 6.292921635, 10.19753198, 12.00781312, 12.22820384, 11.45331980, 7.987282478,  ... and 1, 3.524412954, 0.577259547, -2.198284112, -1.490410178, 1.472307463, 2.232837190, -0.523601767, -3.502786625, -0.840503380, -0.0947136046, 0.3729240434, 1.888078277, 3.875401827, 3.904610349, 1.810281141, 0.220390715,  ... MAPLE k:=3; M:=120; x[0]:=1; y[0]:=1; for n from 1 to M do y[n]:=y[n-1]+k*evalf(sin(x[n-1])); x[n]:=x[n-1]+y[n]; od: [seq(x[n], n=0..M)]; [seq(y[n], n=0..M)]; [seq(floor(x[n]), n=0..M)]; # A320480 CROSSREFS Cf. A320472-A320479. Sequence in context: A274615 A258895 A156890 * A163531 A267095 A016715 Adjacent sequences:  A320477 A320478 A320479 * A320481 A320482 A320483 KEYWORD sign AUTHOR N. J. A. Sloane, Oct 14 2018 STATUS approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)