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Symbolic dynamics for hyperbolic flows
 Amer. J. Math
, 1973
"... Let/, {t e R) be a differentiable flow on a compact manifold M. A compact invariant set A containing no fixed points is called hyperbolic if the tangent bundle restricted to A can be written as the Whitney sum of three Zyjinvariant continuous subbundles TAM = E + Es + Eu, where Eis the onedimensi ..."
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Cited by 118 (0 self)
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the structure of basic sets, namely symbolic dynamics. The space 2 „ = IL{1> • » »} is compact when given the product topology (and {1, •••,«} the discrete topology). One writes x = (#,)£>< » for a point in 2n and x { = {x)t. The shift homeomorphism a:2n> 2n is defined by G{X)ì = Jfy
Applied Symbolic Dynamics*
, 1998
"... Symbolic dynamics is a coarsegrained description of dynamics. By taking into account the geometry of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed not only for onedimensional mappings, unimodal as well as those ..."
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Symbolic dynamics is a coarsegrained description of dynamics. By taking into account the geometry of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed not only for onedimensional mappings, unimodal as well
Forbidden Words in Symbolic Dynamics
, 1999
"... We introduce an equivalence relation ' between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the 'equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the syste ..."
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Cited by 20 (8 self)
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We introduce an equivalence relation ' between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the 'equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant
Symbolic Dynamic Programming
"... A symbolic dynamic programming approach for solving firstorder Markov decision processes within the situation calculus is presented. As an alternative specification language for dynamic worlds the fluent calculus is chosen and the fluent calculus formalization of the symbolic dynamic programming ap ..."
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A symbolic dynamic programming approach for solving firstorder Markov decision processes within the situation calculus is presented. As an alternative specification language for dynamic worlds the fluent calculus is chosen and the fluent calculus formalization of the symbolic dynamic programming
Symbolic dynamics and chaotic synchronization
"... Abstract: Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization ..."
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Abstract: Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization
Computable Symbolic Dynamics
, 2008
"... We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π 0 1 class P is a subshift if and only if there is a computable function F mapping 2 N to 2 N such that P is the set of itineraries of elements of 2 N. Π 0 1 subshifts are construct ..."
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Cited by 3 (0 self)
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We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π 0 1 class P is a subshift if and only if there is a computable function F mapping 2 N to 2 N such that P is the set of itineraries of elements of 2 N. Π 0 1 subshifts
Symbolic dynamics and chaotic synchronization
"... Abstract: Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization [5]. Symbolic dynamics is a rigorous way to investigate chaotic behavior ..."
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Abstract: Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization [5]. Symbolic dynamics is a rigorous way to investigate chaotic
SYMBOLIC DYNAMICS AND THE CATEGORY OF GRAPHS
"... Abstract. Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of nonnegative integers. Sets of these walks are also important in other areas, such as stochastic processes, automata, combinatorial gro ..."
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Abstract. Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of nonnegative integers. Sets of these walks are also important in other areas, such as stochastic processes, automata, combinatorial
Piecewise rotations: symbolic dynamics
"... We consider the piecewise rotation studied in [5], [11] and [9]. If the angle belongs to the set {pi/2, pi/3, pi/6, pi/4, pi/5} we give a complete description of the symbolic dynamics of this map whatever the map is bijective, non injective or non surjective. 1 ..."
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We consider the piecewise rotation studied in [5], [11] and [9]. If the angle belongs to the set {pi/2, pi/3, pi/6, pi/4, pi/5} we give a complete description of the symbolic dynamics of this map whatever the map is bijective, non injective or non surjective. 1
SYMBOLIC DYNAMICS FOR NONHYPERBOLIC SYSTEMS
, 909
"... Abstract. We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space, and they may be used like Markov partitions to ge ..."
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Cited by 2 (1 self)
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to generate symbolic dynamics. Every continuous dynamical system satisfying a weak form of expansiveness possesses an index system. Because of their topological robustness, they can be used to obtain rigorous results from computer approximations of a dynamical system. 1.
Results 1  10
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