Related papers: The Morse index theorem for mechanical systems wit…

We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certain families of closed minimal hypersurfaces in the round…

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical principles by means of differential geometry. Attractive central…

Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…

On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse…

Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…

We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.

This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…

We consider a {\em Hamiltonian setup} $\sextuple$, where $(\mathcal M,\omega)$ is a symplectic manifold, $\mathfrak L$ is a distribution of Lagrangian subspaces in $\mathcal M$, $\mathcal P$ a Lagrangian submanifold of $ \mathcal M$, $H$ is…

In this note we study two index questions. In the first we establish the relationship between the Morse indices of the free time action functional and the fixed time action functional. The second is related to Rabinowitz Floer homology. Our…

In this paper, we generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of regular index filtration for every Morse decomposition.

We investigate the (linearized) Morse index of solutions to Hamiltonan systems, with a focus on convex Hamiltonians functions and sign-changing radial solutions. For strongly coupled systems, we describe the profile of the radial solutions…

The disk complex of a surface in a 3-manifold is used to define its {\it topological index}. Surfaces with well-defined topological index are shown to generalize well-known classes, such as incompressible, strongly irreducible, and critical…

A metallic film of arbitrary thickness is considered. We show that the problem of description of surface plasma oscillations (surface plasmons) with reflection boundary conditions allows analytic solution. Besides, this problem allows…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

In this paper we take an approach similar to that in [M] to establish a positive mass theorem for asymptotically hyperbolic spin manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a…

We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making…

We consider a finite group $G$ acting on a manifold $M$. For any equivariant Morse function, which is a generic condition, there does not always exist an equivariant metric $g$ on $M$ such that the pair $(f,g)$ is Morse-Smale. Here, the…

Morse theoretical ideas are applied to the study of relative equilibria in the planar $n$-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level…

We provide a theory to establish the existence of nonzero solutions of perturbed Hammerstein integral equations with deviated arguments, being our main ingredient the theory of fixed point index. Our approach is fairly general and covers a…