On algebraic Anosov diffeomorphisms on nilmanifolds.
On evolution of small spheres in the phase space of a dynamical system*
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.
On positively expansive differentiable maps
On the rate of mixing of Axiom A flows.
On the unstable directions and Lyapunov exponents of Anosov endomorphisms
Unlike in the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under the transitivity assumption, that an Anosov endomorphism of a closed manifold M is either special (that is, every x ∈ M has only one unstable direction), or for a typical point in M there are infinitely many unstable directions. Another result is the semi-rigidity of the unstable Lyapunov exponent of a codimension one Anosov endomorphism that is C¹-close to a linear endomorphism...
On Ω-stability and structural stability of endomorphisms satisfying Axiom A