For proper cocompact equivariant isometries, the equivariant Fried conjecture holds for suspension flow when the group is compact, when the element has compact centralizer and closed conjugacy class, or when the element is the identity of a discrete group.
On the Minimal Sets of Non-Singular Vector Fields
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The Equivariant Fried Conjecture for Suspension Flow of an Equivariant Isometry
For proper cocompact equivariant isometries, the equivariant Fried conjecture holds for suspension flow when the group is compact, when the element has compact centralizer and closed conjugacy class, or when the element is the identity of a discrete group.