Related papers: Smooth Lyapunov 1-forms

We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We…

In this paper we study an anisotropic expanding flow of smooth, closed, uniformly convex hypersurfaces in $\mathbb{R}^{n+1}$ with speed $\psi\sigma_k(\lambda)^{\alpha}$, where $\alpha$ is a positive constant, $\sigma_k(\lambda)$ is the…

Definition of a smooth action of a CQG on a compact, smooth manifold is given and studied. It is shown that a smooth action is always injective. Furthermore A necessary and sufficient condition for a lift of the smooth action as a bimodule…

We describe necessary and sufficient conditions for an orientation preserving fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.

We present a first-order aggregation model on a group ring, and study its asymptotic dynamics. In a positive coupling strength regime, we show that the flow generated by the proposed model tends to an equilibrium manifold asymptotically.…

We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is…

We prove the existence of solutions of the cohomological equation for the geodesic flow on the unit tangent bundle of a compact flat surface with finitely many cone points. We also prove the ergodicity of the holonomy foliation for surfaces…

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

We study the volume preserving mean curvature flow of a surface immersed in an asymptotically flat $3$-manifold modeling an isolated gravitating system in General Relativity. We show that, if the ambient manifold has positive ADM mass and…

We prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results.

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow…

We present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed including diffusion processes on Riemannian manifolds and Ornstein-Uhlenbeck processes driven by symmetric $\alpha$-stable…

We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…

We consider symplectic cocycles over two classes of partially hyperbolic diffeomorphisms: having compact center leaves and time one maps of Anosov flows. We prove that the Lyapunov exponents are non-zero in an open and dense set in the…

We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed…

We prove that the pluriclosed flow preserves the Vaisman condition on compact complex surfaces if and only if the starting metric has constant scalar curvature.

Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno, Silva and Ruffino ($Stoch$. $Dyn$., 2013) it is shown that, up to a stopping time $\tau$, a stochastic flow of local…

We show that on any Riemannian surface for each $0<c<\infty$ there exists an immersed $C^{1,1}$ curve that is smooth and with curvature equal to $\pm c$ away from a point. We give examples showing that, in general, the regularity of the…

Mishchenko's theorem states that piecewise smooth and Lie algebroid cohomology of a transitive Lie algebroid defined over a combinatorial manifold are isomorphic. In this paper, we describe two applications of that result. The first…

In this article we study topological transitivity of Anosov flows on non-compact 3-manifolds. We provide homological conditions under which the lifts of a transitive Anosov flow to certain infinite covers of the manifold remain transitive.…