Related papers: Stratification of three-dimensional real flows I: …
We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a $3$-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan's homological…
We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
We consider an integrable Hamiltonian system weakly coupled with a pendulum-type system. For each energy level within some range, the uncoupled system is assumed to possess a normally hyperbolic invariant manifold diffeomorphic to a…
We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…
We relate dominated splitting for a linear multiplicative cocyle with dominated splitting for the exterior powers of this cocycle. For a C1 vector field X on a 3-manifold, we can obtain singular-hyperbolicity using only the tangent map DX…
We provide a combinatorial presentation of the set F of 3-dimensional generic flows, namely the set of pairs (M,v) with M a compact oriented 3-manifold and v a nowhere-zero vector field on M having generic behaviour along the boundary of M,…
Given any smooth solenoidal vector field $v_0$ on $\mathbf T^3$, we show the existence of infinitely many H\"older-continuous steady Euler flows $v$ with the same topology as $v_0$, in certain weak sense. In particular, we show that $v$…
It is shown in \cite{yazar6} that a dynamical system defined by a nonvanishing vector field on an orientable three dimensional manifold is globally bi-Hamiltonian if and only if the first Chern class of the normal bundle of the given vector…
We establish the local uniqueness of steady transonic shock solutions with spherical symmetry for the three-dimensional full Euler equations. These transonic shock-fronts are important for understanding transonic shock phenomena in…
We study the soliton flow on the domain of a twistorial harmonic morphism between Riemannian manifolds of dimensions four and three. Assuming real-analyticity, we prove that, for the Gibbons-Hawking construction, any soliton flow is…
We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…
We show that a closed piecewise-linear hypersurface immersed in $R^n$ ($n\ge 3$) is the boundary of a convex body if and only if every point in the interior of each $(n-3)$-face has a neighborhood that lies on the boundary of some convex…
We consider a $\varphi$-rigidity property for divergence-free vector fields in the Euclidean $n$-space, where $\varphi(t)$ is a non-negative convex function vanishing only at $t=0$. We show that this property is always satisfied in…
We consider a closed orientable Riemannian 3-manifold $(M,g)$ and a vector field $X$ with unit norm whose integral curves are geodesics of $g$. Any such vector field determines naturally a 2-plane bundle contained in the kernel of the…
We report a comprehensive numerical study of the renormalization group flow of marginal couplings in $(3+1)$-dimensional projectable Ho\v{r}ava gravity. First, we classify all fixed points of the flow and analyze their stability matrices.…
In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical…
Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However,…
We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact…