动力系统

This article investigates the genericity of ergodic probability measures for the geodesic flow on non-positively curved Riemannian manifolds. We demonstrate that the existence of an open isometric embedding of a product manifold with a…

We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore…

We prove an effective equidistribution theorem for orbits of horospherical subgroups of $\mathrm{SO}(2, 2)$ and $\mathrm{SO}(3, 1)$ in quotients of $\mathrm{SL}_4(\mathbb{R})$ with a polynomial error term. In a forthcoming paper, we will…

This paper investigates the relationship between the solvability of first-order differential equations and the topology of the underlying domain through the lens of de\,Rham cohomology. We analyze the conditions under which a closed 1-form…

Stochastic parameterisations deployed in models of the Earth system frequently invoke locality assumptions such as Markovianity or spatial locality. This work highlights the impact of such assumptions on predictive performance. Both in…

The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker-Smale system with a strictly local communication align to the common mean velocity. In this note we present a partial resolution…

We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its…

This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caract\'eristique'' in the sense of Poincar\'e. Furthermore, we describe the…

We consider symmetric random walks on discrete, Zariski-dense subgroups $\Gamma$ of a semisimple Lie group $G$ with Property (T). We prove that if $\Gamma$ has infinite covolume, then the associated hitting measure on the Furstenberg…

We present a construction of a B\"ottcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the B\"ottcher-type map extends to be continuous on the entire basin of…

We contribute to the thermodynamic formalism of H\"older continuous fiber-bunched matrix cocycles, Anosov diffeomorphisms, and hyperbolic repellers. Specifically, we prove that $1$-typical fiber-bunched cocycles $\mathcal{A}$ over…

This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for…

In this paper, we prove the quasi-compactness of the Frobenius-Perron operator for a piecewise convex map $\tau$ with a countably infinite number of branches on the interval $I=[0,1]$. We establish that for high enough $n$ iterates of…

We consider models of one-dimensional chains of non-nearest neighbor and many-body interacting particles subjected to quasi-periodic media. We extend the results in \cite{12Su&delaLlavelongrange} from analytic to Gevrey regularity…

In the planar $n$-body problem, the problem of infinite spin occurs for both parabolic and collision solutions. Recently Moeckel and Montgomery \cite{MM25} showed that there is no infinite spin for total collision solutions, when the…

We adapt Gou{\"e}zel's pivoting technique to the circle homeomorphism group. As an application, we give different proofs of Gilabert Vio's probabilistic Tits alternative and Malicet's exponential synchronization.

We introduce a two-timescale SIRS-type model in which a fraction $\theta$ of infected individuals experiences a severe course of the disease, requiring hospitalization. During hospitalization, these individuals do not contribute to further…

We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.

This paper focuses on the attitude motion of spacecraft systems featuring asymmetric spacecraft platforms and unbalanced rotors. Through perturbation expansion, the spacecraft dynamic equation is simplified as a linear periodically…

We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally,…