The structure of -limit sets for continuous maps of the interval
We prove that every infinite nowhere dense compact subset of the interval is an -limit set of homoclinic type for a continuous function from to .
The tiered Aubry set for autonomous Lagrangian functions
Let be a Tonelli Lagrangian function (with compact and connected and ). The tiered Aubry set (resp. Mañé set) (resp. ) is the union of the Aubry sets (resp. Mañé sets) (resp. ) for closed 1-form. Then1.the set is closed, connected and if , its intersection with any energy level is connected and chain transitive;2.for generic in the Mañé sense, the sets and have no interior;3.if the interior of is non empty, it contains a dense subset of periodic points.We then give an example...
The topology of holomorphic flows with singularity
The topology of integrable differential forms near a singularity
The zeta functions of Ruelle and Selberg. I
Time Dependent Stable Diffeomorphisms.
Topological and measurable dynamics of Lorenz maps [Book]
Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.
Topological Classification of Linear Endomorphisms.
Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere
This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system obtained via...
Topological pressure for geodesic flows
Topological stability theorem for composite mappings
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.
Topologie du feuilletage fortement stable
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.
Topology and closed characteristics of -contact manifolds.
Topology and dynamics of unstable attractors
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.
Trajectories of polynomial vector fields and ascending chains of polynomial ideals
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...
Transitive flows on manifolds.
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
Transversal homoclinics in nonlinear systems of ordinary differential equations.
Transversely affine foliations of some surface bundles over of pseudo-Anosov type
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.
Travaux de Moser sur la stabilité des mouvements périodiques