TY - JOUR
T1 - Computable chaotic orbits
AU - McCauley, Joseph L.
AU - Palmore, Julian I
PY - 1986/5/12
Y1 - 1986/5/12
N2 - We contrast analytic properties of chaotic maps with the results of fixed-precision computation and then use Turing's ideas of computable irrational numbers to illustrate the computation of chaotic orbits to arbitrary N-bit precision. This leads to the study of chaos theory via integer maps that are automata with long-range site interactions. We also explain why the β-shadowing lemma is not a justification for the use of fixed-precision arithmetic in chaos theory.
AB - We contrast analytic properties of chaotic maps with the results of fixed-precision computation and then use Turing's ideas of computable irrational numbers to illustrate the computation of chaotic orbits to arbitrary N-bit precision. This leads to the study of chaos theory via integer maps that are automata with long-range site interactions. We also explain why the β-shadowing lemma is not a justification for the use of fixed-precision arithmetic in chaos theory.
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U2 - 10.1016/0375-9601(86)90069-1
DO - 10.1016/0375-9601(86)90069-1
M3 - Article
AN - SCOPUS:0001103288
SN - 0375-9601
VL - 115
SP - 433
EP - 436
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 9
ER -