Related papers: A dichotomy for higher dimensional flows
We study continuum-wise expansive flows with fixed points on metric spaces and low dimensional manifolds. We give sufficient conditions for a surface flow to be singular cw-expansive and examples showing that cw-expansivity does not imply…
The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential…
We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e. graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions,…
In this paper we compare a classical finite-difference and a high order finite- volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary…
We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which every regular energy surface is either Anosov or it is in the…
We define the concept of continuum wise expansive for flows, and we prove that continuum wise expansive flows on compact metric spaces with topological dimension greater than one have positive entropy.
We prove that a $C^{\infty}$-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem…
We give a short proof that the ergodic sums of $\mathcal{C}^1$ observables for a $\mathcal{C}^1$ flow on $\mathbb{T}^2$ admitting a closed transversal curve whose Poincar\'e map has constant type rotation number have growth deviating at…
We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly…
In this paper, we consider the volume of a special kind of flow polytope. We show that its volume satisfies a certain system of differential equations, and conversely, the solution of the system of differential equations is unique up to a…
We obtain a dichotomy for $C^1$-generic, volume-preserving diffeomorphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. nonuniformly hyperbolic and the splitting…
We study star flows on closed 3-manifolds and prove that they either have a finite number of attractors or can be $C^1$ approximated by vector fields with orbit-flip homoclinic orbits.
We prove that special flows over an ergodic rotation of the circle under a $C^1$ roof function with one discontinuity do not have local rank one. In particular, any such flow has infinite rank.
We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
We show that every volume preserving codimension one Anosov flow on a closed Riemannian manifold of dimension greater than three admits a global cross section and is therefore topologically conjugate to a suspension of a linear toral…
We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such…
Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is…
We derive representations for finite-dimensional densities of the point processed associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentials appearing in the analog of the Girsanov theorem…
We show that every positive expansive flow on a compact metric space consists of a finite number of periodic orbits and fixed points.