Functions and vector fields on C(CPn)-singular manifolds

Let M2n+1 be a C(CPn) -singular manifold. We study functions and vector fields with isolated singularities on M2n+1. A C(CPn) -singular manifold is obtained from a smooth manifold M2n+1 with boundary in the form of a disjoint union of complex projective spaces CPn boolean OR CPn boolean OR ... boolean OR CPn with subsequent capture of a cone over each component of the boundary. Let M2n+1 be a compact C(CPn) -singular manifold with k singular points. The Euler characteristic of M2n+1 is equal to chi(M2n+1) = k(1 - n)/2. Let M2n+1 be a C(CPn)-singular manifold with singular points m(1), ..., m(k). Suppose that, on M2n+1, there exists an almost smooth vector field V (x) with finite number of zeros m(1), ..., m(k), x(1), ..., x(1). Then chi(M2n+1) = Sigma(l)(i=1) ind(x(i)) + Sigma(k)(i=1) ind(m(i)).

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

Sliding vector fields for non-smooth dynamical systems having intersecting switching manifolds

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

Vector Fields in a Rindler Space

In questo lavoro ci si propone di studiare la quantizzazione del campo vettoriale, massivo e non massivo, in uno spazio-tempo di Rindler, considerando in particolare i gauge di Feynman e assiale. Le equazioni del moto vengono risolte esplicitamente in entrambi i casi; sotto opportune condizioni, è stato inoltre possibile trovare una base completa e ortonormale di soluzioni delle equazioni di campo in termini di modi normali di Fulling. Si è poi analizzata la quantizzazione dei campi vettoriali espressi in questa base.

Survey on haptic rendering of data sets: Exploration of scalar and vector fields

Complementary to automatic extraction processes, Virtual Reality technologies provide an adequate framework to integrate human perception in the exploration of large data sets. In such multisensory system, thanks to intuitive interactions, a user can take advantage of all his perceptual abilities in the exploration task. In this context the haptic perception, coupled to visual rendering, has been investigated for the last two decades, with significant achievements. In this paper, we present a survey related to exploitation of the haptic feedback in exploration of large data sets. For each haptic technique introduced, we describe its principles and its effectiveness.

Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.