Related papers: On the Conley decomposition of Mather sets

This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…

We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called…

We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…

We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter…

The Lee-Friedrichs model has been very useful in the study of decay-scattering systems in the framework of complex quantum mechanics. Since it is exactly soluble, the analytic structure of the amplitudes can be explicitly studied. It is…

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a Hamiltonian description of the theories derived from the…

In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz…

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…

Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…

In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a…

We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.

We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions…

Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.

We introduce a version of Aubry-Mather theory for the length functional of causal curves in compact Lorentzian manifolds. Results include the existence of maximal invariant measures, calibrations and calibrated curves. We prove two versions…

The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.

We study the tau-function and theta-divisor of an isomonodromic family of linear differential (2x2)-systems with non-resonant irregular singularities. In some particular case the estimates for pole orders of the coefficient matrices of the…

An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the…

We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…