相关论文: Good shadows, dynamics, and convex hulls

We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…

In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems $T:X\to X$ where $X$ is a compact metric space and $T$ is Lipschitz continuous. We show that once $T:X\to X$ satisfies both the {\em…

We consider unified dark sector models in which the fluid can collapse and cluster into halos, allowing for hierarchical structure formation to proceed as in standard cosmology. We show that both background evolution and linear…

If G is a countable discrete group acting linearly on a finite-dimensional vector space over any topological field, then the groups of coboundaries are closed for the product topology in all degrees, and hence the cohomology is reduced in…

Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a…

We prove that a C1-generic volume-preserving dynamical system (diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, we prove that the C1-robustness,…

Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…

A defining prediction of the cold dark matter (CDM) cosmological model is the existence of a very large population of low mass haloes, down to planet-size masses. However, their fate as they are accreted onto haloes many orders of magnitude…

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

In this paper we extend to non-compact Riemannian manifolds with boundary the use of two important tools in the geometric analysis of compact spaces, namely, the weak maximum principle for subharmonic functions and the integration by parts.…

We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the…

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…

The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first…

In this work, we derive rigorous and universal bounds on the geometric characteristics of black holes in asymptotically flat spacetimes under assumptions that weak energy condition is satisfied. We prove that the event horizon radius, the…

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We…

In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and…

A consistent theoretical description of physics at high energies requires an assessment of vacuum stability in either the Standard Model or any extension of it. Especially supersymmetric extensions allow for several vacua and the choice of…

Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to…

In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…