Permutation Complexity in Dynamical Systems Ordinal Patterns, Permutation Entropy and All That /

• Κύριος συγγραφέας: Amigó, José (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Σειρά: Springer Series in Synergetics,
• Θέματα: Physics.; Data structures (Computer science).; Applied mathematics.; Engineering mathematics.; Statistical physics.; Dynamical systems.; Statistical Physics, Dynamical Systems and Complexity.; Mathematical Methods in Physics.; Data Structures, Cryptology and Information Theory.; Applications of Mathematics.

 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. 

 What Is This All About? -- First Applications -- Ordinal Patterns -- Ordinal Structure of the Shifts -- Ordinal Structure of the Signed Shifts -- Metric Permutation Entropy -- Topological Permutation Entropy -- Discrete Entropy -- Detection of Determinism -- Space–Time Dynamics -- Conclusion and Outlook.