Dichotomy spectra of triangular equations

Spectra, Spectra, Spectra – Tensor Triangular Spectra versus Zariski Spectra of Endomorphism Rings

We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra ha...

Dichotomy and Fredholm Properties of Evolution Equations

Under minimal assumptions, we characterize the Fredholmity and compute the Fredholm index of abstract differential operators −d/dt + A(·) acting on spaces of functions f : R → X. Here A(t) are (in general) unbounded operators on the Banach space X and our results are formulated in terms of exponential dichotomies on two halflines for the propagtor solving the evolution equation u̇(t) = A(t)u(t) ...

On Exponential Dichotomy of Variational Difference Equations

Universal triangular spectra in parametrically-driven systems

Article history: Received 12 November 2010 Accepted 16 November 2010 Available online 20 November 2010 Communicated by V.M. Agranovich We analyse triangular spectra that appear in many branches of physics that deal with parametricallydriven systems, and give a simple theoretical analysis for them in terms of the nonlinear dynamics of multimode fields. Such spectra appear universally as a result...

Spectra and Systems of Equations

Periodicity properties of sets of nonnegative integers, defined by systems Y = G(Y) of equations, are analyzed. Such systems of set equations arise naturally from equational specifications of combinatorial classes— Compton’s equational specification of monadic second order classes of trees is an important example. In addition to the general theory of set equations and periodicity, with several ...