Dynamics of Topologically Generic Homeomorphisms

By Ethan Akin, M. Hurley, J. Kennedy. 2003

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Turbulence, amalgamation, and generic automorphisms of homogeneous structures (2004, methodology): “7 (Glasner and Weiss [19], Akin, Hurley and Kennedy [3]).”
Chain recurrence rates and topological entropy (2008, background): “(Adding machines arise in many dynamical contexts; see, for example, [3, 7, 8, 9, 18, 20, 23].”
Generically there is but one self homeomorphism of the Cantor set (2006, background): “an open subset of H(X) where the union is taken over all continuous maps φ : X → W. That Cantor space satisﬁes the Rohlin Property was proved by Glasner and Weiss [GW] and by Akin, Hurley and Kennedy [AHK]. We quote the relevant results from the latter. Theorem 3.1. Let X,X1 be Cantor spaces. (a) Fo”
Genericity in topological dynamics (2006, background): “In the present paper we will be concerned with the category of topological dynamics, where there has recently been renewed interest in questions of genericity [2, 3, 6, 12].”
On shadowing: Ordinary and ergodic (2010, background): “There are examples of subshifts of finite type with the shadowing property which are not chain transitive [3].”