We prove that generic convergent diagrams of proper smooth mappings are topologically stable. In proving global properties of diagrams we propose a generalization of the concept of singularity for diagrams, and we establish the geometry of composite mappings.
Soient une variété de Hadamard de courbure et un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de , le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.
This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.
We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coefficients) of the equation and the size of the curve in the space-time, with the exponent depending only on the degree and the dimension.The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned...
In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name
We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.