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The Topological Entropy Conjecture [PDF]
Mathematics, 2021 For a compact Hausdorff space X, let J be the ordered set associated with the set of all finite open covers of X such that there exists nJ, where nJ is the dimension of X associated with ∂. Therefore, we have Hˇp(X;Z), where 0≤p≤n=nJ.
Lvlin Luo
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Uniform entropy vs topological entropy
Topological Algebra and its Applications, 2015 We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.
Dikranjan Dikran, Kunzi Hans-Peter A.
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On the categorical entropy and the topological entropy [PDF]
International Mathematics Research Notices, 2016 To an exact endofunctor of a triangulated category with a split-generator, the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which is a (possibly negative infinite) real-valued function of a real variable.
Kohei Kikuta, A. Takahashi
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On the Topological Entropy of Solenoids [PDF]
Indiana University Mathematics Journal, 1969 James W. England, N. F. G. Martin
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On the Computability of the Topological Entropy of Subshifts [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 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,
Jakob Grue Simonsen
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Topological entropy of block maps [PDF]
Proceedings of the American Mathematical Society, 1980 We show that h ( f ∞ ) = log 2 h({f_\infty }) = \log 2 where f ∞ {f_\infty } is the map on the space of sequences of zeros and ones induced by the block map f
Ethan M. Coven
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Topological entropy for noncompact sets [PDF]
Transactions of the American Mathematical Society, 1973 For f : X → X f:X \to X continuous and Y ⊂ X Y \subset X a topological entropy h ( f , Y ) h(f,Y) is defined.
Rufus Bowen
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Weakly fuzzy topological entropy [PDF]
Mathematica Bohemica, 2022 In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968).
B M Uzzal Afsan
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Universal Lower Bound on Topological Entanglement Entropy. [PDF]
Physical Review Letters, 2023 Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE).
Isaac H. Kim +4 more
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Measuring entanglement entropy and its topological signature for phononic systems [PDF]
Nature Communications, 2023 Entanglement entropy is a fundamental concept with rising importance in various fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective
Zhi-Kang Lin +8 more
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