N. Kh. Rozov

Hyperbolic annulus principle

We study a special class of diffeomorphisms of an annulus (the direct product of a ball in ℝk, k ≥ 2, by an m-dimensional torus). We prove the so-called annulus principle; i.e., we suggest a set of sufficient conditions under which each diffeomorphism in a given class has an m-dimensional expanding hyperbolic attractor.

On the limit values of Mel’nikov functions on periodic orbits

Here e > 0 is a small parameter, the functions H(x, y) and f(t, x, y), g(t, x, y) are jointly infinitely differentiable with respect to (x, y) ∈ G and (t, x, y) ∈ R × G, respectively, where G ⊂ R is some domain. In addition, we assume that the perturbations f and g are periodic in t with some period T0 > 0. The main restrictions under which system (1) will be studied are stated for the limit Hamiltonian system ẋ = H ′ y(x, y), ẏ = −H ′ x(x, y). (2)