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Topological Entropy and Metric Entropy for Regular Impulsive Semiflows
Journal of Dynamics and Differential Equations, 2023Various types of entropy have been defined for measure-theoretic and topological dynamical systems. In the late 1950s, \textit{A. N. Kolmogorov} [Dokl. Akad. Nauk SSSR 119, 861--864 (1958; Zbl 0083.10602)] introduced the \textit{metric entropy} using measurable partitions. In 1965, \textit{R. L. Adler} et al. [Trans. Am. Math. Soc. 114, 309--319 (1965;
Nelda Tamblay +2 more
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Journal of Software Maintenance and Evolution: Research and Practice, 2002
AbstractThis paper presents a new semantically‐based metric for object‐oriented systems, called the Semantic Class Definition Entropy (SCDE) metric, which examines the implementation domain content of a class to measure class complexity. The domain content is determined using a knowledge‐based program understanding system.
Etzkorn, Letha H. +2 more
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AbstractThis paper presents a new semantically‐based metric for object‐oriented systems, called the Semantic Class Definition Entropy (SCDE) metric, which examines the implementation domain content of a class to measure class complexity. The domain content is determined using a knowledge‐based program understanding system.
Etzkorn, Letha H. +2 more
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The Metric Entropy of Endomorphisms
Communications in Mathematical Physics, 2009\(M\) is a compact connected Riemannian manifold and \(f: M \rightarrow M\) is a \(C^2\) non-invertible but non-degenerate endomorphism After giving some basic notions and properties about forward Lyapunov metric, inverse limit space of (M.f), entropies in this space and partitions subordinate to the stable manifolds, the author proves that an \(f ...
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Gaussian Approximation Numbers and Metric Entropy
Journal of Mathematical Sciences, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kühn, T., Linde, W.
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Computing Invariant Densities and Metric Entropy
Communications in Mathematical Physics, 2000This paper deals with the absolutely continuous invariant measure \(\mu\) for a piecewise analytic expanding Markov map \(T\) of the interval. The authors present a method for accurately computing the Lyapunov exponent of \(\mu\). The authors construct atomic signed measures \(\mu_M\) supported on periodic orbits up to period \(M\), and prove that ...
Pollicott, Mark, Jenkinson, Oliver
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Metric Entropy and Topological Entropy
2012This chapter is dedicated to the study of metric entropy, including its relation to topological entropy. After establishing some basic properties of metric entropy, we consider the notion of conditional entropy, and we show how generators can be used to compute metric entropy. We then establish the Shannon–McMillan–Breiman theorem, which can be seen as
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2010
The word “entropy” was coined by the German physicist R. Clausius (1822–1888), who introduced it in thermodynamics in 1865 to measure the amount of energy in a system that cannot produce work. The fact that the entropy of an isolated system never decreases constitutes the second law of thermodynamics and clearly shows the central role of entropy in ...
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The word “entropy” was coined by the German physicist R. Clausius (1822–1888), who introduced it in thermodynamics in 1865 to measure the amount of energy in a system that cannot produce work. The fact that the entropy of an isolated system never decreases constitutes the second law of thermodynamics and clearly shows the central role of entropy in ...
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