Nonsingular Group Actions

Weak Mixing Properties for Nonsingular Actions

For a general group G we consider various weak mixing properties of nonsingular actions. In the case where the action is actually measure preserving all these properties coincide, and our purpose here is to check which implications persist in the nonsingular case.

The C Closing Lemma for Nonsingular Endomorphisms Equivariant under Free Actions of Finite Groups

In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.

Property (T) and the Furstenberg Entropy of Nonsingular Actions

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure μ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg μ-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condit...

Characterizing Mildly Mixing Actions by Orbit Equivalence of Products

We characterize mildly mixing group actions of a noncompact locally compact second countable group G using orbit equivalence We show an amenable action of G is mildly mixing if and only if G is amenable and for any nonsingular ergodic G action the product G action is orbit equivalent to We extend the result to the case of nite measure preserving noninvertible endomorphisms i e when G N and show...

Maharam Extension for Nonsingular Group Actions