Related papers: Decomposition of Spectral flow and Bott-type Itera…
Let A be an arbitrary set. For any transformation T (self-map of A) let T(f)(x):=f(T(x)) (for all x in A) be the usual shift operator. A function g is called periodic, i.e., invariant mod T, if Tg=g (=Ig, where I is the identity operator).…
We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
We consider families of strongly indefinite systems of elliptic PDE and investigate bifurcation from a trivial branch of solutions by using the spectral flow. The novelty in our approach is a refined version of a comparison principle that…
Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative…
We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t = \xi_t…
Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno, Silva and Ruffino ($Stoch$. $Dyn$., 2013) it is shown that, up to a stopping time $\tau$, a stochastic flow of local…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in…
Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this…
In the framework of Lie transform and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…
We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an…
In this paper we present a decomposition algorithm for computation of the spatial-temporal optical flow of a dynamic image sequence. We consider several applications, such as the extraction of temporal motion features and motion detection…
In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action…
We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{\xi_1,...,\xi_s\}$. We use this sequence to…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…
Let $\{A(t)\}_{t \in \mathbb{R}}$ be a path of self-adjoint Fredholm operators in a Hilbert space $\mathcal{H}$, joining endpoints $A_\pm$ as $t \to \pm \infty$. Computing the index of the operator $D_A= (d/d t) + A$ acting in…
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm…