A local variational relation and applications

By Wen Huang, Xiangdong Ye. 2006

153 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/08e103b5ad5f9e57c0e2b47da10b406e9045f342

How researchers see this paper

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

In Geometry and Topology

1. Xiangdong Ye
2. Eli Glasner
3. Jian Li
4. Wen Huang
5. David Kerr
6. Hanfeng Li
7. Guohua Zhang
8. S. Shao

In Mathematical Physics

1. Xiangdong Ye
2. Wen Huang
3. Eli Glasner
4. Hanfeng Li
5. Jian Li
6. David Kerr
7. Guohua Zhang
8. A. Dooley

Citations in the corpus

• Measure-theoretical sensitivity and equicontinuity (2011, background): “Proof. (1) It was shown in [ 23 ] that (xi) n=1 ∈ En(X, T) iff, for every product neighborhood n=1 Ui of (xi) n=1 , there is a sequence J ⊂ Z+ with positive”
• Recent development of chaos theory in topological dynamics (2015, methodology): “It was first proved by Huang and Ye using the notion of interpolating sets [49], and we state it here using the notion of independence by Kerr and Li [53].”
• 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].”
• A PANORAMA OF SPECIFICATION-LIKE PROPERTIES AND THEIR CONSEQUENCES (2015, background): “Huang and Ye [42] introduced the notion of a topological K-system.”
• Independence in topological and C*-dynamics (2006, background): “1”
• Local Entropy Theory of a Random Dynamical System (2011, methodology): “4 we can prove (the proof follows ideas from [28, 32, 34, 36, 37] and is quite standard, and so we shall omit it, for details see [28, 32, 34, 36, 37] or §12 of the paper): Theorem 13.”
• Stable sets and mean Li–Yorke chaos in positive entropy systems (2012, background): “For every n ≥ 2, define a measure l n ( m ) on ( X ( n ) , T ( n ) ) by letting where m It is well known that when m is ergodic with positive entropy (see for example [4, 18]), m x is non-atomic for m -a.e x ∈ X and l n ( m ) is a T ( n ) -invariant ergodic measure on X ( n ) .”
• Homoclinic groups, IE groups, and expansive algebraic actions (2011, background): “[7–10,24,26,31–35]), and has been found to be related to combinatorial independence [39,40], which appeared first in Rosenthal’s [69] work on Banach spaces containing 1.”
• Infinite-step nilsystems, independence and complexity (2011, background): “In [22], entropy pairs are characterized as those pairs that admit an interpolating set of positive density.”
• Mean equicontinuity and mean sensitivity (2013, background): “[22, 23] Let (X, T ) be a dynamical system.”
• Combinatorial lemmas and applications to dynamics (2009, background): “In [18] the authors were able to extend the notions from pairs to finite tuples (for recent results concern-”
• Local entropy theory (2009, methodology): “Also note that there exists a TDS which is upe of order two but is not upe of order three [59].”
• Combinatorial Independence and Sofic Entropy (2012, methodology): “(3) A continuous action Gy X of a discrete amenable group on a compact Hausdorff space has positive topological entropy if and only if it has a nondiagonal IE-pair (for G = Z this was first proved by Huang and Ye in [21] using measure-theoretic techniques).”