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A review of symbolic dynamics and symbolic reconstruction of dynamical systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of ...
Yoshito Hirata, José M. Amigó
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2010
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type.
B��al, Marie-Pierre +3 more
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This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type.
B��al, Marie-Pierre +3 more
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Augmented dynamic symbolic execution
Proceedings of the 27th IEEE/ACM International Conference on Automated Software Engineering, 2012Dynamic symbolic execution (DSE) can efficiently explore all simple paths through a program, reliably determining whether there are any program crashes or violations of assertions or code contracts. However, if such automated oracles do not exist, the traditional approach is to present the developer a small and representative set of tests in order to ...
Konrad Jamrozik +3 more
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Mathematical Logic Quarterly, 2008
AbstractWe investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ.
Cenzer, Douglas +2 more
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AbstractWe investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ.
Cenzer, Douglas +2 more
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Symbolic dynamics in cardiotocographic monitoring
2013 E-Health and Bioengineering Conference (EHB), 2013-Foetal heart rate variability is considered an important parameter, capable to highlight foetal reactivity and wellbeing. Many studies focused their attention on foetal heart rate variability analysis, using different techniques both in time and frequency domain.
ROMANO, MARIA +6 more
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Symbolic Dynamics for Smale Flows
American Journal of Mathematics, 1987The author develops a symbolic model for a certain class of flows. The model is the suspension of a subshift of finite type by a continuous function. The class of flows for which this is developd is strictly larger than the class of axiom A flows where this type of construction was carried out by Bowen. The author calls these flows Smale flows.
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Symbolic Dynamics for IFS Attractors
Fractals, 1997It has recently been shown that a modified iterated function system (IFS) is capable of generating closed orbits which undergo bifurcation and transition to a chaotic regime as control parameters are varied.1,2 Here we show that driving such an IFS by a partition of itself creates maps which can be characterized by a symbolic dynamics. Forbidden words
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1988
In a sense the method of symbolic dynamics(1) is the only mathematically rigorous approach to the study of chaotic behavior in dynamical systems. However, having its roots in the topological theory of dynamical systems, symbolic dynamics remains a rather abstract chapter of mathematics and still seems to be useless for a practical physicist. The aim of
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In a sense the method of symbolic dynamics(1) is the only mathematically rigorous approach to the study of chaotic behavior in dynamical systems. However, having its roots in the topological theory of dynamical systems, symbolic dynamics remains a rather abstract chapter of mathematics and still seems to be useless for a practical physicist. The aim of
openaire +1 more source