Measure-theoretical sensitivity and equicontinuity

By Wen Huang, Ping Lu, Xiangdong Ye. 2011

94 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3116f8939619f57be5f308eb1e403daf866850a3

How researchers see this paper

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

In Applied Mathematics

1. Felipe Garc'ia-Ramos
2. Eli Glasner
3. Xiangdong Ye
4. Jian Li
5. Wen Huang
6. J. Thouvenot

In Geometry and Topology

1. Xiangdong Ye
2. Jian Li
3. Felipe Garc'ia-Ramos
4. Wen Huang
5. Eli Glasner
6. S. Shao
7. Tomasz Downarowicz
8. Siming Tu

In Mathematical Physics

1. Xiangdong Ye
2. Jian Li
3. Wen Huang
4. Felipe Garc'ia-Ramos
5. Eli Glasner
6. S. Shao
7. Tomasz Downarowicz
8. Siming Tu

Citations in the corpus

• Local entropy theory (2009, methodology): “Together with results from Huang et al [54] and Huang and Ye [57], one can show that a minimal topological K -system is strongly mixing.”
• Nil Bohr-sets and almost automorphy of higher order (2014, background): “(2) N(x, U) ∈ F∗d,0 for each neighborhood U of y. (3) N(x, U) ∈ FPoid for each neighborhood U of y. (4) N(x, U) ∈ FBird for each neighborhood U of y. (5) N(x, U) ∈ FSGd for each neighborhood U of y. (6) N(x, U) ∈ FBd for each neighborhood U of y. (7) N(x, U) ∈ FPd for each neighborhood U of y.”
• Bounded complexity, mean equicontinuity and discrete spectrum (2018, methodology): “It was shown in [8] that if (X ,T) is μ-equicontinuous and μ is ergodic then μ has discrete spectrum.”
• Recent development of chaos theory in topological dynamics (2015, background): “[42] developed a theory of sensitive sets, which measures the “degree” of sensitivity both in the topological and the measure-theoretical setting.”
• Isomorphic extensions and applications (2015, background): “Huang, Lu and Ye [16] introduce a hybrid notion of μ-equicontinuity (of a topological system with a fixed invariant measure μ) and prove that this property implies discrete spectrum of (X,μ, T ).”
• Mean equicontinuity and mean sensitivity (2013, background): “(2) The authors in [19] have studied equicontinuous subsets and equicontinuity with respect to an invariant measure.”
• Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, methodology): “Measure-theoretical results Measure-theoretical equicontinuity for TDSs with respect to Borel probability measures has been studied in [7, 12, 15, 24].”