Independence in topological and C*-dynamics

By David Kerr, Hanfeng Li. 2006

253 citations recorded by the source corpus.

We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties. We also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to C*-dynamics.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8521e3d174b8d7dc93ce9ba4453e93e28108d78a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Combinatorial Independence and Sofic Entropy (2012, background): “4(2) in [21] uniformly nonnull (every pair is an IN-pair)”
Local entropy theory (2009, methodology): “The following lemma obtained in [60] is an extension of the Kerr-Li lemma in [74].”
Stable sets and mean Li–Yorke chaos in positive entropy systems (2012, methodology): “Moreover, the authors in [19] proved that the intersection of the set of Li-Yorke pairs with the set of entropy pairs is dense in the set of entropy pairs.”
Mean equicontinuity and mean sensitivity (2013, background): “[22, 23] Let (X, T ) be a dynamical system.”
The structure of tame minimal dynamical systems (2006, methodology): “In fact, Kerr and Li in their work [ 18 ], use independence to unify the theory of these various notions and in particular they are able to characterize tame systems (which they call regular) as those systems that (in some precise sense) do not admit inflnite independence sets ([18, Proposition”
Homoclinic groups, IE groups, and expansive algebraic actions (2011, background): “terminologies in [39,40].”
On invariant measures for B-free systems (2014, unknown): “The B-free subshifts turn out to be hereditary systems [8], i.”
Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, background): “In Kerr and Li [26], the relationship between independence and entropy was studied.”
The Chowla and the Sarnak conjectures from ergodic theory point of view (2014, background): “To see this, we need first to recall the following definition [15]: Definition 5.”
Local entropy theory for a countable discrete amenable group action (2010, background): “From then on, the local entropy theory of Z-actions have been made great achievements [1, 2, 3, 4, 5, 11, 16, 21, 23, 24, 25, 27, 40, 46], see also the relevant chapters in [17] and the survey papers [19, 20].”
Combinatorial lemmas and applications to dynamics (2009, background): “3 in [24].”
Recurrence properties and disjointness on the induced spaces (2013, result): “A remarkable result by Glasner and Weiss [8] stated that the t opological entropy of (X,T) is zero if and only if so is(M(X),TM) (similar results related to nullness and tameness can be found in [13, 14]).”
Infinite-step nilsystems, independence and complexity (2011, background): “In [24], it is shown that (X, T ) is a null system if and only if it contains no non-trivial IN-pairs.”
Local Entropy Theory of a Random Dynamical System (2011, background): “m to all countable discrete amenable group actions. Local entropy theory for inﬁnite countable discrete amenable group actions has been systematically studied by Huang, Ye and Zhang [37]. Kerr and Li [40] studied independence of such actions using combinatorial methods. Global entropy theory for ame”
Measure-theoretical sensitivity and equicontinuity (2011, background): “density such that i∈J T −i Us(i) � ∅ for any s ∈{ 1 ,...,n } J .M oreover, it was proved in [ 26 ] that (xi) n=1 ∈ SEn(X, T) iff, for every product neighborhood n=1 Ui of (xi) n=1 , there are arbitrarily long finite subsets J ⊂ Z+ such”