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On the computability of the topological entropy of subshifts
 Discrete Math. Theor. Comput. Sci
"... We prove that the topological entropy of subshifts having decidable language is uncomputable in the following sense: For no error bound less than 1/4 does there exists a program that, given a decision procedure for the language of a subshift as input, will approximate the entropy of the subshift wit ..."
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Cited by 3 (1 self)
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We prove that the topological entropy of subshifts having decidable language is uncomputable in the following sense: For no error bound less than 1/4 does there exists a program that, given a decision procedure for the language of a subshift as input, will approximate the entropy of the subshift
Topological entropy for appropriately approximated
 J. Math. Phys
, 1994
"... Abstract. The “classical ” topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author’s recent development of a non–commutative generalization of topological entropy, in the natural setting of general C ∗ –algebras as the non–commutative c ..."
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Cited by 9 (0 self)
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Abstract. The “classical ” topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author’s recent development of a non–commutative generalization of topological entropy, in the natural setting of general C ∗ –algebras as the non
ON THE TOPOLOGICAL ENTROPY OF FAMILIES OF BRAIDS
, 808
"... Abstract. A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov’s coordinates on the boundary of Teichmüller space, is described. The method is illustrated on two twoparameter families of braids. 1. ..."
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Cited by 5 (0 self)
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Abstract. A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov’s coordinates on the boundary of Teichmüller space, is described. The method is illustrated on two twoparameter families of braids. 1.
On the Estimation of Topological Entropy
 Journal of Statistical Physics
, 1993
"... We study here a method for estimating the topological entropy of a smooth dynamical system. Our method is based on estimating the logarithmic growth rates of suitably chosen curves in the system. We present two algorithms for this purpose and we analyze each according to its strengths and pitfalls. ..."
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Cited by 15 (1 self)
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We study here a method for estimating the topological entropy of a smooth dynamical system. Our method is based on estimating the logarithmic growth rates of suitably chosen curves in the system. We present two algorithms for this purpose and we analyze each according to its strengths and pitfalls
Relating topological entropy and measure entropy
 Bull. London Math. Soc
, 1971
"... In [1] the notion of topological entropy was introduced as a flowisomorphism invariant. It was conjectured that topological entropy was the supremum of the measure entropies taken over all invariant regular Borel probability measures. This conjecture has been verified by E. I. Dinaburg [2] for a ho ..."
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Cited by 21 (1 self)
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In [1] the notion of topological entropy was introduced as a flowisomorphism invariant. It was conjectured that topological entropy was the supremum of the measure entropies taken over all invariant regular Borel probability measures. This conjecture has been verified by E. I. Dinaburg [2] for a
topological entropy rigorously
, 2006
"... Our automatic method developed for the detection of chaos is used for finding rigorous lower bounds for the topological entropy of the classical Hénon mapping. We do this within the abstract framework created by Galias and Zgliczynski in 2001, and focus on covering graphs involving different iterati ..."
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Our automatic method developed for the detection of chaos is used for finding rigorous lower bounds for the topological entropy of the classical Hénon mapping. We do this within the abstract framework created by Galias and Zgliczynski in 2001, and focus on covering graphs involving different
Billiards With Positive Topological Entropy
, 2001
"... We prove that billiard flows on strictly convex tables with a sufficiently small circular scatterer generically admit positive topological entropy. In particular we show that billiard systems in nonconcentric circular annuli have the same property for sufficiently small inner radii in both eucli ..."
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Cited by 3 (0 self)
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We prove that billiard flows on strictly convex tables with a sufficiently small circular scatterer generically admit positive topological entropy. In particular we show that billiard systems in nonconcentric circular annuli have the same property for sufficiently small inner radii in both
TOPOLOGICAL ENTROPY AND PARTIALLY HYPERBOLIC
, 2006
"... Abstract. We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique nontrivial homologies. We prove the following two results: if the center foliation is one dimensional, then the topological entropy is locally a constant; ..."
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Abstract. We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique nontrivial homologies. We prove the following two results: if the center foliation is one dimensional, then the topological entropy is locally a constant
On the topological entropy of saturated sets
 Ergod. Th. & Dynam. Sys
"... Abstract Let (X, d, T ) be a dynamical system, where (X, d) is a compact metric space and T : X → X a continuous map. We introduce two conditions for the set of orbits, called respectively galmost product property and uniform separation property. The galmost product property holds for dynamical s ..."
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Cited by 7 (0 self)
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systems with the specification property, but also for many others. For example all βshifts have the galmost product property. The uniform separation property is true for expansive and more generally asymptotically hexpansive maps. Under these two conditions we compute the topological entropy
Results 1  10
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1,184