Search results for "Topological conjugacy"

A note on renewal systems

1992

Abstract A renewal system is a symbolic dynamical system generated by free concatenations of a finite set of words. In this paper we prove that, given two systems which are both renewal and Markov systems, it is decidable whether they are topologically conjugate. The proof makes use of the methods and the techniques of formal language theory.

Generalized iterated function systems on the spacel∞(X)

2014

Abstract In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space X I into X , where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.

Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

A simple algorithm for generating neuronal dendritic trees

1990

Abstract A simple, efficient algorithm is presented for generating the codewords of all neuronal dendritic trees with a given number of terminal nodes. Furthermore, a procedure is developed for deciding if different codewords correspond to topologically equivalent trees.

MBPT for the Green's function

2013

Combinatorial Models in the Topological Classification of Singularities of Mappings

2018

The topological classification of finitely determined map germs \(f:(\mathbb R^n,0)\rightarrow (\mathbb R^p,0)\) is discrete (by a theorem due to R. Thom), hence we want to obtain combinatorial models which codify all the topological information of the map germ f. According to Fukuda’s work, the topology of such germs is determined by the link, which is obtained by taking the intersection of the image of f with a small enough sphere centered at the origin. If \(f^{-1}(0)=\{0\}\), then the link is a topologically stable map \(\gamma :S^{n-1}\rightarrow S^{p-1}\) (or stable if (n, p) are nice dimensions) and f is topologically equivalent to the cone of \(\gamma \). When \(f^{-1}(0)\ne \{0\}\)…

Plane foliations with a saddle singularity

2012

Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.

Transitive Anosov flows and Axiom-A diffeomorphisms

2009

AbstractLet M be a smooth compact Riemannian manifold without boundary, and ϕ:M×ℝ→M a transitive Anosov flow. We prove that if the time-one map of ϕ is C1-approximated by Axiom-A diffeomorphisms with more than one attractor, then ϕ is topologically equivalent to the suspension of an Anosov diffeomorphism.

Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles

1995

AbstractWe consider Anosov flows on closed 3-manifolds. We show that if such a flow admits a weak foliation whose lifting in the universal covering is a product foliation, thenit is characterized up to topological equivalence by its weak stable foliation up to topological conjugacy. As a corollary we obtain that, up to topological equivalence and finite coverings, suspensions and geodesic flows are the unique Anosov flows on closed 3-manifolds whose weak stable foliations are transversely projective.

Hyperbolicity as an obstruction to smoothability for one-dimensional actions

2017

Ghys and Sergiescu proved in the $80$s that Thompson's group $T$, and hence $F$, admits actions by $C^{\infty}$ diffeomorphisms of the circle . They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of piecewise projective homeomorphisms, and Lodha-Moore defined finitely presentable groups of piecewise projective homeomorphisms. These groups are of particular interest because they are nonamenable and contain no free subgroup. In contrast to the result of Ghys-Sergiescu, we prove that the groups of Monod and Lodha-Moore are not topologically conjugate to a group of $C^1$ diffeomorphisms. Fur…