On the principle of stability of invariance of physical systems
On the problem of stability for near to integrable Hamiltonian systems.
On the quasiconformal surgery of rational functions
On the question of stability in a Hamiltonian system
On the rate of mixing of Axiom A flows.
On the relationship between hyperbolic and cone-hyperbolic structures in metric spaces
We give necessary and sufficient conditions for topological hyperbolicity of a homeomorphism of a metric space, restricted to a given compact invariant set. These conditions are related to the existence of an appropriate finite covering of this set and a corresponding cone-hyperbolic graph-directed iterated function system.
On the spectral flow and the index theorem for flat vector bundles
On the stability of elliptic equilibria.
On the stabilization of internally coupled map lattice systems.
On the structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval.
On the structure of the space of continuous maps with zero topological entropy
On the topology of solenoidal attractors of the cylinder
On the uniqueness of the fixed point index on differentiable manifolds.
On the ω-limit sets of tent maps
For a continuous map f on a compact metric space (X,d), a set D ⊂ X is internally chain transitive if for every x,y ∈ D and every δ > 0 there is a sequence of points ⟨x = x₀,x₁,...,xₙ = y⟩ such that for 0 ≤ i< n. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an ω-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed,...
On top spaces.
On Topological Stability of Divergent Diagrams of Folds.
On two-parametric systems of matrices and diffeomorphisms
On univoque points for self-similar sets
Let K ⊆ ℝ be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method...
On zeta function and scattering poles for several convex bodies
On Ω-stability and structural stability of endomorphisms satisfying Axiom A