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|a 9783642040849
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|a Amigó, José
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| 245 |
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|a Permutation Complexity in Dynamical Systems
|h Elektronische Ressource
|b Ordinal Patterns, Permutation Entropy and All That
|c by José Amigó
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| 250 |
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|a 1st ed. 2010
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2010, 2010
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| 300 |
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|a X, 280 p. 13 illus. in color
|b online resource
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|a 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
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| 653 |
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|a Complex Systems
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| 653 |
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|a Data Structures and Information Theory
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| 653 |
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|a System theory
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| 653 |
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|a Information theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Data structures (Computer science)
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| 653 |
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|a Applications of Mathematics
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| 653 |
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|a Mathematics
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| 653 |
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|a Theoretical, Mathematical and Computational Physics
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| 653 |
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|a Mathematical Methods in Physics
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|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Springer Series in Synergetics
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| 028 |
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|a 10.1007/978-3-642-04084-9
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| 856 |
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|u https://doi.org/10.1007/978-3-642-04084-9?nosfx=y
|x Verlag
|3 Volltext
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|a 530.1
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|a 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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