Related papers: Dynamics forced by surface trellises

The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set. We see, in particular, that some topological conditions are sufficient to guarantee that these sets…

We survey some recent advances in the study of (area-preserving) flows on surfaces, in particular on the typical dynamical, ergodic and spectral properties of smooth area-preserving (or locally Hamiltonian) flows, as well as recent…

Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…

Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

We study the orbit behavior of a four dimensional smooth symplectic diffeomorphism $f$ near a homoclinic orbit $\Gamma$ to an 1-elliptic fixed point under some natural genericity assumptions. 1-elliptic fixed point has two real eigenvalues…

We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp…

In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments are presented. They are constructed via familiar crystal nets using edges as geometric scaffolds for n-fold helical windings.…

Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…

Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic…

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…

Triply degenerate fixed points appear in global bifurcations -- homoclinic and heteroclinic tangencies. In order to get Lorenz-like attractors, the dynamics of the first return map along the homoclinic or heteroclinic cycle should be…

Flexible structures in an incoming perpendicular flow typically undergo elastic reconfiguration that reduces drag; however, at higher velocities, they are prone to dynamical instabilities that entail complex wake dynamics and fluctuating…

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…

This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a…

The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its…

We show that any weakly partially hyperbolic diffeomorphism on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly partially hyperbolic system. We also construct examples of…