TY - JOUR
T1 - Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series
AU - Bollt, Erik M.
AU - Stanford, Theodore
AU - Lai, Ying-Cheng
AU - Zyczkowski, Karol
PY - 2000/10/16
Y1 - 2000/10/16
N2 - This paper investigates the consequence of misplaced partitions in chaotic systems. Specifically, it addresses how the topological entropy, perhaps one of the most important dynamical invariants that one intends to compute from symbolic dynamics, behaves as a parameter, d, which characterizes the amount of misplaced partition, is changed. It is found that the topological entropy as a function of d is devil's staircase-like, but surprisingly nonmonotone. Results are established by performing numerical computations for 1D and 2D maps and by rigorous analyses for the tent map.
AB - This paper investigates the consequence of misplaced partitions in chaotic systems. Specifically, it addresses how the topological entropy, perhaps one of the most important dynamical invariants that one intends to compute from symbolic dynamics, behaves as a parameter, d, which characterizes the amount of misplaced partition, is changed. It is found that the topological entropy as a function of d is devil's staircase-like, but surprisingly nonmonotone. Results are established by performing numerical computations for 1D and 2D maps and by rigorous analyses for the tent map.
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U2 - 10.1103/PhysRevLett.85.3524
DO - 10.1103/PhysRevLett.85.3524
M3 - Article
AN - SCOPUS:0034300534
SN - 0031-9007
VL - 85
SP - 3524
EP - 3527
JO - Physical Review Letters
JF - Physical Review Letters
IS - 16
ER -