相关论文: Non-minimizing connecting orbits for multi-well sy…

Using area-preserving curve shortening flow, and a new inequality relating the potential generated by a set to its curvature, we study a non-local isoperimetric problem which arises in the study of di-block copolymer melts, also referred to…

In this paper we study the dynamics near the equilibrium point of a family of Hamiltonian systems in the neighborhood of a $0^2 iw$ resonance. The existence of a family of periodic orbits surrounding the equilibrium is well-known and we…

Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry…

We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…

In a previous article, we define "connectivity weights" to be functions with these two properties: 1) They solve the three conformal Ward identities of conformal field theory (CFT) and a system of $2N$ null-state differential equations…

In this paper we study the existence of periodic orbits with prescribed energy levels of convex Lagrangian systems on complete Riemannian manifolds. We extend the existence results of Contreras by developing a modified minimax principal to…

We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by…

The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…

We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…

A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied with taking into account the minimization of the corresponding integral functional. Such integral, as being not sequentially weakly…

We establish a novel connection between the minimal nilpotent orbit $\mathbb{O}_n$ in $\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\overline{\mathbf{O}}_n$ in $\mathfrak{so}_{2n+2}$, which differs from the shared-orbit…

The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical points, i.e. we do not assume that critical points are…

We construct a complete invariant for non-wandering surface flows with finitely many singular points but without locally dense orbits. Precisely, we show that a flow $v$ with finitely many singular points on a compact connected surface $S$…

Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of $\Gamma$-symmetric systems $\ddot q(t)=-\nabla U(q(t))$ in any neighborhood of an isolated orbit of minima $\Gamma(q_0)$…

Let $(M,g)$ be a closed Riemannian manifold, $L: TM\rightarrow \mathbb R$ be a Tonelli Lagrangian. Given two closed submanifolds $Q_0$ and $Q_1$ of $M$ and a real number $k$, we study the existence of Euler-Lagrange orbits with energy $k$…

The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric…

Motivated by the problem of global stability of thermodynamical equilibria in non-equilibrium thermodynamics formulated in a recent paper [12], we introduce some mechanisms for constructing semi-infinite orbits of contact Hamiltonian…

Let f be a polynomial or a rational function which has r summable critical points. We prove that there exists an r-dimensional manifold in an appropriate space containing f such that for every smooth curve in it through f, the ratio between…

Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for connections that are invariant under a Lie group action on the manifold with orbits of codimension less than or equal…

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…