A320474 - OEIS

%I #15 Oct 15 2018 05:05:55

%S 1,2,4,6,7,9,11,12,13,15,17,18,20,22,24,25,26,28,30,31,32,34,36,37,38,

%T 40,42,43,45,47,49,50,51,53,55,56,57,59,61,62,63,65,67,68,70,71,74,75,

%U 76,78,80,81,83,85,87,88,89,91,93,94,95,96,99,100,101,103,105,106,108,110,112,113,114,116,118,119,120,122

%N a(n) = floor(x(n)), where (x(n),y(n)) are defined by the Chirikov "standard map" y(n) = y(n-1) + sin(x(n-1)), x(n) = x(n-1) + y(n), with x(0)=y(0)=1.

%C 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.

%C Note that some websites reduce x(n) mod 2*Pi, but this version does not.

%D H. A. Lauwerier, Two-dimensional iterative maps, Chapter 4 of A. V. Holden, ed., Chaos, Princeton, 1986. See Eq. (4.67).

%D E. N. Lorenz, The Essence of Chaos, Univ. Washington Press, 1993. See p 191.

%H Roderick V. Jensen, <a href="https://www.jstor.org/stable/27854538">Classical chaos</a>, American Scientist 75.2 (1987): 168-181. See Eq. (2), (3).

%e The initial values of x(n) and y(n) are

%e 1, 2.841470985, 4.978578409, 6.150905537, 7.191338328, 9.020139937, 11.24262759, 12.49547800, 13.67749516, 15.75571048, 17.78619673, 18.94269021, 20.19218340, 22.41575881, 24.22736856, ...

%e and

%e 1, 1.841470985, 2.137107424, 1.172327128, 1.040432791, 1.828801609, 2.222487650, 1.252850411, 1.182017163, 2.078215324, 2.030486252, 1.156493480, 1.249493186, 2.223575410, 1.811609751, ...

%p k:=1; M:=120; x[0]:=1; y[0]:=1;

%p for n from 1 to M do

%p y[n]:=y[n-1]+k*evalf(sin(x[n-1]));

%p x[n]:=x[n-1]+y[n];

%p od:

%p [seq(x[n],n=0..M)];

%p [seq(y[n],n=0..M)];

%p [seq(floor(x[n]),n=0..M)]; # A320494

%Y Cf. A320472-A320480.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 14 2018