Related papers: Dynamically ordered energy function for Morse-Smal…
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function $H$ and a Casimir $C$ of the corresponding Lie algebra. The orbits of the system are included in…
We consider weak solutions to the incompressible Euler equations. It is shown that energy conservation holds in any Onsager critical class in which smooth functions are dense. The argument is independent of the specific critical regularity…
The paper is devoted to study the Dirichelet energy of moving frames on 2-dimensional tori immersed in the euclidean $3\leq m$-dimensional space. This functional, called Frame energy, is naturally linked to the Willmore energy of the…
We prove the existence of a continuous Morse energy function for an arbitrary topological flow with finite hyperbolic (in topological sense) chain recurrent set on a topological manifold of any dimension. This result is a partial solution…
We describe generating functions for arbitrary-genus Gromov-Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing…
We obtain the dynamic correlation function of two-dimensional lattice gas with nearest-neighbor repulsion in ordered c(2$\times$2) phase (antiferromagnetic ordering) under the condition of low concentration of structural defects. It is…
Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…
We prove that among the set of smooth diffeomorphisms there exists a $C^1$-open and dense subset of data such that either the Lagrange spectrum is finite and the dynamics is a Morse-Smale diffeomorphism or the Lagrange spectrum has positive…
The classical electromagnetic self-force on an arbitrary time-dependent electric or magnetic dipole moving with constant velocity in vacuum, and in a medium, is considered. Of course, in vacuum there is no net force on such a particle.…
We analyse the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin condition for the…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
In this work, we consider wormhole geometries in third-order Lovelock gravity and investigate the possibility that these solutions satisfy the energy conditions. In this framework, by applying a specific equation of state, we obtain exact…
We investigate saddle point configurations in spherical ferromagnets with perpendicular anisotropy. These are modeled by a micromagnetic energy functional on the unit sphere that leads to the emergence of the so-called curvature induced…
For a closed oriented 3-manifold $Y$ we define $n(Y)$ to be the minimal non-negative number such that in each homotopy class of non-singular vector fields of $Y$ there is a Morse-Smale vector field with less or equal to $n(Y)$ periodic…
In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using…
We demonstrate existence of topologically nontrivial energy minimizing maps of a given positive degree from bounded domains in the plane to $\mathbb S^2$ in a variational model describing magnetizations in ultrathin ferromagnetic films with…
We study the dynamical Myers effect by allowing the fuzzy (or the dynamical dielectric brane) coordinates to be time dependent. We find three novel kinds of the dynamical spherical dielectric branes depending on their respective excess…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of $\mathbb{D}^{2}$, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the…
Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits outside the chain-recurrent set. In this paper we show that we…