On mostly expanding diffeomorphisms

On Structurally Stable Diffeomorphisms with Codimension One Expanding Attractors

We show that if a closed n-manifold Mn (n ≥ 3) admits a structurally stable diffeomorphism f with an orientable expanding attractor Ω of codimension one, then Mn is homotopy equivalent to the n-torus Tn and is homeomorphic to Tn for n 6= 4. Moreover, there are no nontrivial basic sets of f different from Ω. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having ...

On Groups of Diffeomorphisms

I. We consider here the groups of homeomorphisms on Euclidean w-space and the «-sphere Sn. Chiefly we will be concerned with the question of whether or not these groups reduce in an homotopy sense to the ordinary orthogonal group acting on these spaces. Such questions are intimately connected with the theory of fibre bundles in which these spaces occur as fibres. We will restrict ourselves to t...

Diffeomorphisms on the Torus

For orientation-reversing diffeomorphisms on the torus necessary and sufficient conditions are given for an isotopy class to admit a Morse-Smale diffeomorphism with a specified periodic behavior. A diffeomorphism is Morse-Smale provided it is structurally stable and has a finite nonwandering set [P-S]. Several recent papers have explored the relationship between the topology of these maps and t...

Gibbs-markov Structures and Limit Laws for Partially Hyperbolic Attractors with Mostly Expanding Central Direction

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = E cu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achiev...

SRB measures for partially hyperbolic systems whose central direction is mostly expanding