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Analogues of Takens’ theorems for generalized actions of the group ℤ


The notion of a generalized action of the group ℤ on a topological space generated by an arbitrary countable family of pairwise commuting homeomorphisms is introduced, and a study of generalized orbits under such actions is given. Analogues of Takens’ theorems on the genericity of the maximal and minimal ɛ-equivalences for such actions are obtained.

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Correspondence to N. A. Begun.

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Original Russian Text © N.A. Begun, S.Yu. Pilyugin, 2010, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2010, No. 4, pp. 10–16.

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Begun, N.A., Pilyugin, S.Y. Analogues of Takens’ theorems for generalized actions of the group ℤ . Vestnik St.Petersb. Univ.Math. 43, 198–203 (2010).

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  • generalized action
  • generalized orbit
  • maximal and minimal equivalences