相关论文: Attractors and orbit-flip homoclinic orbits for st…

We prove that every sectional Anosov flow (or, equivalently, every sectional-hyperbolic attracting set of a flow) on a compact manifold has a periodic orbit. This extends the previous three-dimensional result obtained in [Existence of…

We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting…

The stellar velocity fields of elliptical galaxies hold clues to their dynamical structure and origin. The construction of velocity field models is greatly simplified by assuming an approximate geometrical form for the streamlines of the…

We prove that simply connected H-surfaces with small diameter in a 3-manifold necessarily concentrate at a critical point of the scalar curvature.

In this paper we study the homotopical rotation vectors and the homotopical rotation sets for the billiard flow on the unit flat torus with three, mutually intersecting and mutually orthogonal cylindrical scatterers removed from it. The…

It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct…

Given two elements of a vector space acted on by a reductive group, we ask whether they lie in the same orbit, and if not, whether one lies in the orbit closure of the other. We develop techniques to optimize the orbit and orbit closure…

Many fully convective stars exhibit a wide variety of surface magnetism, including starspots and chromospheric activity. The manner by which bundles of magnetic field traverse portions of the convection zone to emerge at the stellar surface…

We consider the bifurcation diagram in a suitable parameter plane of a quadratic vector field in $\mathbb{R}^3$ that features a homoclinic flip bifurcation of the most complicated type. This codimension-two bifurcation is characterized by a…

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a…

In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In…

We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…

We consider the topological behaviors of continuous maps with one topological attractor on compact metric space $X$. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals…

In this review, analytical results obtained for a wide class of stationary axisymmetric flows in the vicinity of compact astrophysical objects are analyzed, with an emphasis on quantitative predictions for specific sources. Recent years…

We show that every positive expansive flow on a compact metric space consists of a finite number of periodic orbits and fixed points.

We study a cosmological model of gravity coupled to three, self-interacting scalar fields, one of them with negative kinetic term. The theory has cosmological solutions described by three-dimensional quadratic autonomous equations, leading…

A new relation between homoclinic points and Lagrangian Floer homology is presented: In dimension two, we construct a Floer homology generated by primary homoclinic points. We compute two examples and prove an invariance theorem. Moreover,…

Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in…

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of…

Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is…