Masayuki Asaoka

Hyperbolic sets exhibiting ¹-persistent homoclinic tangency for higher dimensions

For any manifold of dimension at least three, we give a simple construction of a hyperbolic invariant set that exhibits C1-persistent homoclinic tangency. It provides an open subset of the space of C 1 -diffeomorphisms in which generic diffeomorphisms have arbitrary given growth of the number of attracting periodic orbits and admit no symbolic extensions.

Deformation of Locally Free Actions and Leafwise Cohomology

These are the notes of the author’s lectures at the Advanced Course on Foliations in the research program Foliations, which was held at the Centre de Recerca Matematica in May 2010. In these notes, we discuss the relationship between deformations of actions of Lie groups and the leafwise cohomology of the orbit foliation.

A {C^\infty} closing lemma for Hamiltonian diffeomorphisms of closed surfaces

We prove a

Erratum to "Hyperbolic sets exhibiting C^1 -persistent homoclinic tangency for higher dimensions''

{C^\infty}

Homotopy classes of total foliations

C∞ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a

Nonhomogeneous locally free actions of the affine group

{C^\infty}