Topological entropy

By Roy L. Adler, Tomasz Downarowicz, M. Misiurewicz. Scholarpedia, 2008

808 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/30e24a72af1f65e717880772918b4e44c02a7a3c

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In Artificial Intelligence

Citations in the corpus

Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “Entropy is an important numerical invariant of actions defined for Γ = Z by Kolmogorov, Sinǎı, Adler-Konheim-MacAndrew (see [26],[44],[1]) and for amenable groups by Kieffer and Ornstein-Weiss (see [25],[35]).”
Dynamical Degrees, Arithmetic Degrees, and Canonical Heights for Dominant Rational Self-Maps of Projective Space (2011, neutral): “Indeed, the map in Example 16 applied to the point P = [1, 2, 1] provides an example with ĥφ(P ) = 0 and αφ(P ) = δφ.”
Recent development of chaos theory in topological dynamics (2015, background): “The notions of topological entropy and weakmixing were introduced by Adler et al [1] in 1965 and Furstenberg [25] in 1967 respectively.”
Communication Requirement for Reliable and Secure State Estimation and Control in Smart Grid (2011, methodology): “The main mathematical tool is the topological entropy [1], which is a measure of the complexity of the dynamic system.”
Variational principles for topological entropies of subsets (2010, background): “The quantity hUCtop (T ,Z) is the straightforward generalization of the Adler–Konheim–McAndrew definition [1] of the topological entropy to arbitrary subsets.”
Dynamical systems and categories (2013, background): “Also, when T is Z/2-graded in the sense that [2] ∼= idT, only the value at zero, δ0(E1, E2), will be of any use.”
Soficity, amenability, and dynamical entropy (2010, methodology): “We begin by recalling the classical definition of topological entropy [1, 12].”
MULTIPLE PERIODIC SOLUTIONS AND COMPLEX DYNAMICS FOR SECOND ORDER ODES VIA LINKED TWIST MAPS (2007, background): “As proved in [1], σ has positive topological entropy, given by”
Local entropy theory (2009, background): “In 1965 Adler et al [1] defined topological entropy for TDSs.”
Entropy and the variational principle for actions of sofic groups (2010, neutral): “It follows by the variational principle of Section 6 and the classical variational principle that, for a continuous action of a countable amenable group on a compact metrizable space, the sofic topological entropy with respect to any sofic approximation sequence is equal to the classical topological”
Entropy on abelian groups (2010, methodology): “We recall the definition of the topological entropy following [1].”