TY - JOUR
T1 - Editorial
AU - Amigó, José M.
AU - Keller, Karsten
AU - Kurths, Jürgen
PY - 2013/6/1
Y1 - 2013/6/1
N2 - Symbolic dynamics is a powerful tool in the study of dynamical systems. The purpose of symbolic dynamics is to provide a simplified picture of complicated dynamics, that gives some insight into its complexity. To this end, the state space of the system is partitioned in a finite number of pieces, and the exact trajectories of individual points are traded off by the trajectory relative to that partition. These so-called coarse-grained trajectories turn out to be realisations of a stationary random process with a finite alphabet. In particular, the entropy of a dynamical system can be approximated by the Shannon entropy of any of its symbolic dynamics (the finer the partition, the better the approximation). Today, symbolic dynamics is an independent field of theoretical physics and applied mathematics with applications to such important disciplines as cryptology, time series analysis, and data-compression.
AB - Symbolic dynamics is a powerful tool in the study of dynamical systems. The purpose of symbolic dynamics is to provide a simplified picture of complicated dynamics, that gives some insight into its complexity. To this end, the state space of the system is partitioned in a finite number of pieces, and the exact trajectories of individual points are traded off by the trajectory relative to that partition. These so-called coarse-grained trajectories turn out to be realisations of a stationary random process with a finite alphabet. In particular, the entropy of a dynamical system can be approximated by the Shannon entropy of any of its symbolic dynamics (the finer the partition, the better the approximation). Today, symbolic dynamics is an independent field of theoretical physics and applied mathematics with applications to such important disciplines as cryptology, time series analysis, and data-compression.
UR - http://www.scopus.com/inward/record.url?scp=84879704632&partnerID=8YFLogxK
U2 - 10.1140/epjst/e2013-01839-6
DO - 10.1140/epjst/e2013-01839-6
M3 - Editorial
AN - SCOPUS:84879704632
SN - 1951-6355
VL - 222
SP - 241
EP - 247
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 2
ER -