Related papers: Smooth and F--smooth systems

We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and…

We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of…

We study smooth fibrations of compact torsion-free Spin(7)-manifolds by Cayley submanifolds. Using geometric and topological constraints coming from the Spin(7)-structure, we show that only two topological configurations can arise. One of…

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the…

In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth…

Often topological classes of one-dimensional dynamical systems are finite codimension smooth manifolds. We describe a method to prove this sort of statement that we believe can be applied in many settings. In this work we will implement it…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth manifolds. Round fold maps were introduced as stable fold…

Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The corresponding notion for nonlinear systems is that of…

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…

A Seifert manifold is a 3-dimensional manifold with a circle action. It is a circle bundle (with singularities) over a 2-dimensional orbifold. In this note, we discuss a generalized Seifert manifolds. By definition, they have bundle-like…

This article examines a family of smooth mappings between Banach spaces and establishes conditions for the existence of their zeros. Applications to fixed-point problems and the Implicit Function Theorem are also discussed.

Given a field of Hilbert spaces there are two ways to endow it with a smooth structure: the standard and geometrical notion of Hilbert (or Hermitian) bundle and the analytical notion of smooth field of Hilbert spaces. We study the…

Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water- and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system…

Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…

The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical…

In the present paper, we study bi-$f$-harmonic maps which generalize not only $f$-harmonic maps, but also biharmonic maps. We derive bi-$f$-harmonic equations for curves in the Euclidean space, unit sphere, hyperbolic space, and in…

We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…

We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in $\RR^2$ through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the…

In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Along these hypersurfaces one describes the metrics in terms of…

We extend some known results from smooth dynamical systems to the category of Lipschitz homeomorphisms of compact metric spaces. We consider dynamical properties as robust expansiveness and structural stability allowing Lipschitz…