Mean topological dimension

By Elon Lindenstrauss, Barak Weiss. 2000

393 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6a4d209e3d25a75ba500e3dbd5b63ef802d4f65d

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In Computational Theory and Mathematics

1. Xiangdong Ye
2. Wen Huang
3. Alain Miranville
4. Sergey Zelik
5. Hanfeng Li
6. Guohua Zhang
7. David Kerr
8. Yonatan Gutman

In Mathematical Physics

1. David Kerr
2. G'abor Szab'o
3. W. Winter
4. Wen Huang
5. Xiangdong Ye
6. Hanfeng Li
7. Guohua Zhang
8. Z. Niu

In Numerical Analysis

1. Yonatan Gutman
2. David Kerr
3. Sergey Zelik
4. Alain Miranville
5. Hanfeng Li
6. J. Giol
7. Tomasz Downarowicz
8. Lai-Sang Young

Citations in the corpus

• Local entropy theory for a countable discrete amenable group action (2010, background): “…n 1 , n i , δ )-invariant and ′ m | δ , thus by Lemma 2.1 the right translates of F n k that lie in F ′ m form a δ -even cover of F ′ m , and so by Lemma 2.2 there exists By the same reasoning there exists Moreover, by (2.1) and (2.2) we have The following lemma is proved in [30, Theorem 6.1].”
• Fuglede--Kadison determinants and entropy for actions of discrete amenable groups (2005, background): “y monotonicity. For an open cover U of Xlet N(U) be the cardinality of a minimal subcover of U. For a finite subset Fof Γ let UF = _ γ∈F γU be the common refinement of the finitely many covers γU. Using [LW] Theorem 6.1 one sees that the limit h(U) = lim n→∞ 1 |F n| logN(UFn) exists and is independent ”
• Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, background): “, for spatial dynamics and spatial chaos), such an invariant exists, namely, the so-called mean topological dimension introduced in [142] (for the Bernoulli scheme with a continuous number of symbols) which can be obtained as in Definition 5.”
• Subshifts and perforation (2010, methodology): “When Y has nonzero topological dimension the system (X,T ) has nonzero mean dimension (see Section 3 of [18]), and in this case the uncountability of the set of extreme points also follows from the fact that Z-systems with nonzero mean dimension do not possess the small boundary property [18, Thm.”
• Variational principles for topological entropies of subsets (2010, background): “For an invertible TDS (X,T ), Lindenstrauss and Weiss [25] introduced the mean dimension mdim(X,T ) (an idea suggested by Gromov).”
• The C∗-algebra of a minimal homeomorphism of zero mean dimension (2014, background): “(Presumably, mean dimension zero!) In the present note we show that the condition of finite dimension can be replaced by the weaker condition that the dynamical system has mean dimension zero, as defined in [10] (Definition 2.”
• Mean dimension and Jaworski‐type theorems (2012, methodology): “Mean dimension was introduced by Gromov [6] and systematically investigated by Lindenstrauss and Weiss [19].”
• Entropy in dynamical systems (2003, background): “been long known for homeomorphism of finite entropy as a consequence of the theory of mean dimension created by Elon Lindenstrauss and Benjy Weiss [Lindenstrauss and Weiss, 2000; Lindenstrauss, 1999].”