Related papers: The Morse index theorem for regular Lagrangian sys…

We develop an index theory for parabolic and collision solutions to the classical n-body problem and we prove sufficient conditions for the finiteness of the spectral index valid in a large class of trajectories ending with a total collapse…

We prove a Wong-Rosay type theorem for a domain with a piecewise smooth generic strictly pseudoconvex boundary point.

In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…

We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For the minimal surfaces…

A recent generalization of the Conley index to discrete multivalued dynamical systems without a continuous selector is motivated by applications to data-driven dynamics. In the present paper we continue the program by studying…

This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…

Using morphic cohomology, we produce a sequence of conjectures, called morphic conjectures, which terminates at the Grothendieck standard conjecture A. A refinement of Hodge structures is given, and with the assumption of morphic…

We prove the Morse relations for the set of all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of every geodesic…

Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of…

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…

We prove an index theorem for the quotient module of a monomial ideal. We obtain this result by resolving the monomial ideal by a sequence of Bergman space like essentially normal Hilbert modules.

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…

The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of…

We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.

We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a topological assumption, a critical point…

Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…

We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of…

This paper studies linear relations and their self-adjoint realizations arising from 2d-dimensional canonical systems, with a focus on how the symplectic structure interacts with boundary conditions. Understanding this interplay allows us…

We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie…

Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setting of combinatorial and classical dynamical systems. We…