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The study of permutation complexity can be envisioned as a new kind
of symbolic dynamics whose basic blocks are ordinal patterns, that
is, permutations defined by the order relations among points in the
orbits of dynamical systems. Since its inception in 2002 the
concept of permutation entropy has sparked a new branch of research
in particular regarding the time series analysis of dynamical
systems that capitalizes on the order structure of the state space.
Indeed, on one hand ordinal patterns and periodic points are
closely related, yet ordinal patterns are amenable to numerical
methods, while periodicity is not. Another interesting feature is
that since it can be shown that random (unconstrained) dynamics has
no forbidden patterns with probability one, their existence can be
used as a fingerprint to identify any deterministic origin of orbit
generation. This book is primarily addressed to researchers working
in the field of nonlinear dynamics and complex systems, yet will
also be suitable for graduate students interested in these
subjects. The presentation is a compromise between mathematical
rigor and pedagogical approach. Accordingly, some of the more
mathematical background needed for more in depth understanding has
been shifted into the appendices.
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