Examples of diffeomorphism

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The map f is a nice diffeomorphism if it is nice at both ends.
Moreover, we not only obtain a dominated splitting, but also the fact that the diffeomorphism is hyperbolic or partially hyperbolic.
This map is continuous and is a diffeomorphism on the interior.
Is it possible for a minimal set of a diffeomorphism of a two-dimensional manifold to carry an invariant mixing measure?
Assume that f is a twist diffeomorphism on the torus.
We construct a diffeomorphism preserving a non-hyperbolic measure whose pointwise dimension does not exist almost everywhere.
In general, the stable and unstable foliations of a partially hyperbolic diffeomorphism do not have to be quasi-isometric.
They accumulate on another invariant circle on which the induced diffeomorphism has an irrational rotation number.
Here these hypotheses are replaced by the assumption that f is a nice diffeomorphism in between the critical points.
Due to the high speed of the convergence, this remains true for sufficiently long orbit segments of the limit diffeomorphism.
Invariant measures for a diffeomorphism which expands the leaves of a foliation.
Still, the conformal volume-preserving group has infinite codimension in the full diffeomorphism group and staying in it may confer some advantage.
Given a twist diffeomorphism f on the torus without a rotationalinvariant circle, there exist infinitely many periodic orbits with non-zero shear-rotation number.
This is the first known example of a stably ergodic diffeomorphism that is not structurally stable.

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