Local entropy theory

By Eli Glasner, Xiangdong Ye. Ergodic Theory and Dynamical Systems, 2009

100 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/aa614d441e5979ed87822034d2f889815e95f282

How researchers see this paper

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

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Topological chaos: what may this mean? (2008, background): “For a more complete view of the theory the reader may consult books such as [1,3,19,24,27,40]; in addition many other notions that may be significant are described in a recent survey on local entropy [29].”
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].”
Homoclinic groups, IE groups, and expansive algebraic actions (2011, methodology): “We refer the readers to [24, 26] for a nice account for the case Γ = Z.”
Infinite-step nilsystems, independence and complexity (2011, background): “The first one comes from the so called local entropy theory, for a survey see [12].”
Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, background): “It is an open question whether every transitive null Z+-system is minimal (see [17, 23]).”
Recent development of chaos theory in topological dynamics (2015, background): “We refer the reader to [28, 103] for more information on topological entropy, and [31] for a survey of local entropy theory.”
Stable sets and mean Li–Yorke chaos in positive entropy systems (2012, background): “Nowadays, the idea of using various tuples to obtain dynamical properties is widely accepted and developed, see for example the surveys [15, 24].”
Sufficient conditions under which a transitive system is chaotic (2009, methodology): “We refer the reader to the recent monograph [AAG08] and the review [ GY08 ] on local entropy theory, which include discussions of the above”
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.”
Combinatorial Independence and Sofic Entropy (2012, unknown): “Inspired by work in the local theory of entropy [19], the authors studied this connection between independence, weak mixing, and entropy in [24, 25] as part of a program to develop a general theory of combinatorial independence in dynamics.”