Mean equicontinuity and mean sensitivity

By Jian Li, Siming Tu, Xiangdong Ye. Ergodic Theory and Dynamical Systems, 2013

143 citations recorded by the source corpus.

Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are obtained when a dynamical system is transitive or minimal. Localizing the notion of mean equicontinuity, notions of almost mean equicontinuity and almost Banach mean equicontinuity are introduced. It turns out that a system with the former property may have positive entropy and meanwhile a system with the latter property must have zero entropy.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/388f5e44344d195601e8b70548f6ec8dfa687d7d

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. Jian Li
2. Felipe Garc'ia-Ramos
3. Xiangdong Ye
4. Wen Huang
5. Leiye Xu
6. J. Thouvenot
7. Eli Glasner
8. Guohua Zhang

In Mathematical Physics

1. Jian Li
2. Xiangdong Ye
3. Felipe Garc'ia-Ramos
4. Wen Huang
5. J. Thouvenot
6. Leiye Xu
7. Eli Glasner
8. Guohua Zhang

In Statistical and Nonlinear Physics

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

Citations in the corpus

• Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, methodology): “This question has been independently solved directly in [31] using different tools.”
• Bounded complexity, mean equicontinuity and discrete spectrum (2018, methodology): “For works related to mean equicontinuity, we refer to [7, 13, 14, 25, 26].”