Related papers: A note on the divergence-free Jacobian Conjecture …

We give for the first time a detailed proof of the Palamodov's total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture posed by Lyapunov and Arnold and reduces the Lagrange-Dirichlet…

The classical criterion of Jensen for the Riemann hypothesis is that all of the associated Jensen polynomials have only real zeros. We find a new version of this criterion, using linear combinations of Hermite polynomials, and show that…

We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The…

Let $F:\mathbb{C}[x_1,\ldots,x_n] \to \mathbb{C}[x_1,\ldots,x_n]$ be a $\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the…

We perform the study of the stability of the cosmological scalar field models, by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In the KCC approach we describe the time evolution of the scalar field…

We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary…

This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…

In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…

For a homeomorphism with $p$-integrable distortion, we obtain the optimal global degree of integrability for the reciprocal of its Jacobian determinant. As an application, we strengthen the result of Dole\v{z}alov\'a, Hencl and Mal\'y…

We prove the Arnold conjecture for closed symplectic manifolds with $\pi_2(M)=0$ and $\cat M=\dim M$. Furthermore, we prove an analog of the Lusternik-Schnirelmann theorem for functions with ``generalized hyperbolicity'' property.

This article has two purposes. The first is to prove solutions of the second boundary value problem for generated Jacobian equations are strictly $g$-convex. The second is to prove the global $C^3$ regularity of Aleksandrov solutions to the…

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…

We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and…

It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then…

We consider the asymptotics of orthogonal polynomials for measures that are differentiable, but not necessarily analytic, multiplicative perturbations of Jacobi-like measures supported on disjoint intervals. We analyze the Fokas-Its-Kitaev…

The main result of this paper is to prove the strong real Jacobian conjecture under the symmetric assumption and reveals the link between it and the Jacobian conjecture. Precisely, we assume that $F: \mathbb{R}^n \to \mathbb{R}^n$ is of…

Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re equations arising in optimal transport. In this paper, we introduce and study a damped…

We prove the global well-posedness and scattering for the 3D incompressible Euler-Coriolis system with sufficiently small, regular and suitably localized initial data. Equivalently, we obtain the asymptotic stability for "rigid body"…

We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological…