Essential curves in handlebodies and topological contractions

If $X$ is a compact set, a {\it topological contraction} is a self-embedding $f$ such that the intersection of the successive images $f^k(X)$, $k>0$, consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus $\geq 2$ whose image is essential. Our proof is based on an easy criterion for a simple curve to be essential in a handlebody

On heteroclinic separators of magnetic fields in electrically conducting fluids

In this paper we partly solve the problem of existence of separators of a magnetic field in plasma. We single out in plasma a 3-body with a boundary in which the movement of plasma is of special kind which we call an (a-d)-motion. We prove that if the body is the 3-annulus or the "fat" orientable surface with two holes the magnetic field necessarily have a heteroclinic separator. The statement of the problem and the suggested method for its solution lead to some theoretical problems from Dynamical Systems Theory which are of interest of their own

Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds

This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding conditions to the existence of such an energy function, that is, a function whose set of critical points coincides with the non-wandering set of the considered diffeomorphism. We show that the necessary and sufficient conditions to the existence of a dynamically ordered energy function reduces to the type of embedding of one-dimensional attractors and repellers of a given Morse-Smale diffeomorphism on a closed 3-manifold

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Contemporary percutaneous treatment of unprotected left main coronary stenoses: initial results from a multicenter registry analysis 1994-1996.

BACKGROUND: Coronary artery bypass surgery (CABG) has been considered the therapy of choice for patients with unprotected left main (ULMT) coronary stenoses. Selected single-center reports suggest that the results of percutaneous intervention may now approach those of CABG. METHODS AND RESULTS: To assess the results of percutaneous ULMT treatment from a wide variety of experienced interventional centers, we requested data on consecutive patients treated after January 1, 1994, from 25 centers. One hundred seven patients were identified who were treated either electively (n=91) or for acute myocardial infarction (n=16). Of patients treated electively, 25% were considered inoperable, and 27% were considered high risk for bypass surgery. Primary treatment included stents (50%), directional atherectomy (24%), and balloon angioplasty (20%). Follow-up was 98.8% complete at 15+/-8 months. Results varied considerably, depending on presentation and treatment. For patient