Let M be a smooth manifold and let F be a codimension one, C foliation on M , with isolated singularities of Morse type. The study and classification of pairs (M,F) is a challenging (and difficult) problem. In this setting, a classical result due to Reeb [Reeb] states that a manifold admitting a foliation with exactly two centertype singularities is a sphere. In particular this is true if the f...

We consider an autonomous system admitting invariant manifold M. The following questions are discussed: (i) what the conditions ensuring exponential stability of manifold? (ii) does every motion attracting by M tend to some on (i.e. have asymptotic phase)? (iii) is geometrical structure set formed orbits approaching a given orbit? get answer in terms Lyapunov functions omitting assumption that ...

Let R be an associative ring with center Z(R) , I a nonzero ideal of and  be automorphism  of . An 3-additive mapping M:RxRxR is called symmetric left -3-centralizer if M(u1y,u2 ,u3)=M(u1,u2,u3)(y) holds for all  y, u1, u2, u3 In this paper we shall investigate the  commutativity prime rings admitting satisfying any one following conditions : (i)M([u ,y], u3)  [(u), (y)...

A packing of a graph G is a set {G1, G2} such that G1 ∼= G, G2 ∼= G, and G1 and G2 are edge disjoint subgraphs of Kn. Let F be a family of graphs. A near packing admitting F of a graph G is a generalization of a packing. In a near packing admitting F , the two copies of G may overlap so the subgraph defined by the edges common to both copies is a member of F . In the paper we study three famili...

Abst ract A homoclinic orbit is considered for which the center-stable and center-unstable manifolds of a saddle-node equilibrium have a quadratic tangency. This bifurcation is of codimension two and leads generically to the creation of a bifurcation curve deening two independent transverse homoclinic orbits to a saddle-node. This latter case was shown by L.P. Shilnikov to imply shift dynamics....

The goal of this article is to establish several general properties a somewhat large class partially hyperbolic diffeomorphisms called discretized Anosov flows. A definition for these systems presented and proven be equivalent with the introduced in [1], as well notion flow type [13].The set flows shown $ C^1 $-open closed inside diffeomorphisms. Every dynamically coherent plaque expansive. Uni...

This paper deals with variational inclusions of the form: 0 ∈ f(x)+F (x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ∈ f(xk)+ ∑M i=1 ai∇f ( xk+βi(xk+1−xk) ) (xk+1−xk)+F (xk+1) where the single-valued function involved in this relation is an approximation of the ...

A few years ago, the first example of a closed manifold admitting an Anosov diffeomorphism but no expanding map was given. Unfortunately, this is not explicit and high-dimensional, although its exact dimension unknown due to type construction. In paper, we present family concrete 12-dimensional nilmanifolds with map, where nilmanifold defined as quotient 1-connected nilpotent Lie group by cocom...