Null systems and sequence entropy pairs

By Wen Huang, Shujun Li, S. Shao, Xiangdong Ye. Ergodic Theory and Dynamical Systems, 2003

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Local entropy theory (2009, background): “In [48] it was shown that a minimal null system is an almost one-to-one extension of an equicontinuous system.”
Combinatorial lemmas and applications to dynamics (2009, background): “1 implies that maximal pattern entropy n-tuples are the same as sequence entropy n-tuples, and maximal pattern entropy n-tuples for μ are the same as sequence entropy n-tuples for μ (see [16,17]).”
Independence in topological and C*-dynamics (2006, background): “1”
Tame systems and scrambled pairs under an Abelian group action (2006, background): “To this aim, we need to introduce the notion of weakly mixing pairs (which notion was first introduced and studied by Huang et al in [16]).”
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.”
Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, background): “Since minimal null systems are almost automorphic [23], we obtain that minimal null subshifts are regular almost automorphic (Corollary 67).”