Uniform structures and the equivalence of diffeomorphisms

A new equivalence relation between diffeomorphisms of a compact manifold, viz., $\delta$-equivalence, is defined on the basis of concepts in uniform topology. The $\delta$-equivalence classes of the identity map, the $Y$-diffeomorphisms of infra-nullmanifolds, and the connection between $\delta$-equivalence and topological entropy are studied. The proofs make use of an effective description of the uniform-homotopy type of the “nonautonomous suspensions over diffeomorphisms” described in the paper. The connection between diffeomorphisms and non-autonomous flows is considered; moreover, the nonhomotopy of the $Y$-diffeomorphism of the identity map is proved.