Nullness is equivalent to polynomial maximal pattern complexity, equicontinuity to bounded pattern complexity, and transitive nonminimal null systems exist with prescribed rigidity and scattering properties.
von Neumann,Zur Theorie der Gesellschaftsspiele, Math
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Maximal pattern complexity and structure of null systems
Nullness is equivalent to polynomial maximal pattern complexity, equicontinuity to bounded pattern complexity, and transitive nonminimal null systems exist with prescribed rigidity and scattering properties.