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.
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, 3.682941970, 5.335298253, 5.363285286, 3.800190225, 1.013078481, -0.077102958, -1.321337570, -4.503664553, -5.729399487, -5.903312461, -5.335620669, -3.143935907, ...
and
1, 2.682941970, 1.652356283, 0.027987033, -1.563095061, -2.787111744, -1.090181439, -1.244234612, -3.182326983, -1.225734934, -0.173912974, 0.5676917924, 2.191684762, ...
MAPLE
k:=2; 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(round(x[n]), n=0..M)]; # A320475
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Oct 14 2018
STATUS
approved