TY - JOUR
T1 - Estimating generating partitions of chaotic systems by unstable periodic orbits
AU - Davidchack, Ruslan L.
AU - Lai, Ying-Cheng
AU - Bollt, Erik M.
AU - Dhamala, Mukeshwar
PY - 2000
Y1 - 2000
N2 - An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.
AB - An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.
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U2 - 10.1103/PhysRevE.61.1353
DO - 10.1103/PhysRevE.61.1353
M3 - Article
AN - SCOPUS:0001167045
SN - 1063-651X
VL - 61
SP - 1353
EP - 1356
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 2
ER -