We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions...We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.展开更多
In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti numbe...In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale–Williams solenoids.展开更多
Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spac...Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces （possibly S3） branched over （1, 1）-knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3-sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper.展开更多
文摘We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.
文摘In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale–Williams solenoids.
文摘Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces （possibly S3） branched over （1, 1）-knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3-sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper.
