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On asymmetry of the future and the past for limit self-joinings

2003; American Mathematical Society; Volume: 131; Issue: 7 Linguagem: Inglês

10.1090/s0002-9939-03-06796-0

1088-6826

Oleg N. Ageev,

Advanced Differential Equations and Dynamical Systems

Let $\triangle _T$ be an off-diagonal joining of a transformation $T$. We construct a non-typical transformation having asymmetry between limit sets of $\triangle _{T^n}$ for positive and negative powers of $T$. It follows from a correspondence between subpolymorphisms and positive operators, and from the structure of limit polynomial operators. We apply this technique to find all polynomial operators of degree $1$ in the weak closure (in the space of positive operators on $L_2$) of powers of Chacon’s automorphism and its generalizations.