80 resultados para Polynomial vector field
Resumo:
In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.
Resumo:
This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.
Resumo:
We investigate in this paper the topological stability of pairs (omega, X), where w is a germ of an integrable 1-form and X is a germ of a vector field tangent to the foliation determined by omega.
Resumo:
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)).
Resumo:
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Resumo:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Resumo:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Resumo:
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Resumo:
Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).
Resumo:
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Resumo:
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Resumo:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Resumo:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Resumo:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Resumo:
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)