Now showing items 1-6 of 6
On the injectivity of C1 maps of the real plane
(Canadian Journal of Mathematics, 2002-12-01) [Artigo]
Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to ...
On the dynamics of the Bianchi IX system
(Journal of Physics A: Mathematical and Theoretical, 2007-06-29) [Artigo]
In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic ...
Regularization of discontinuous vector fields on R-3 via singular perturbation
(Journal of Dynamics and Differential Equations, 2007-06-01) [Artigo]
Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira ...
On the global dynamics of the Rabinovich system
(Journal of Physics A: Mathematical and Theoretical, 2008-07-11) [Artigo]
In this paper by using the Poincare compactification in R(3) make a global analysis of the Rabinovich system(x) over dot = hy - v(1)x + yz, (y) over dot = hx - v(2)y - xz, (z) over dot = -v(3)z + xy,with (x, y, z) is an ...
Periodic orbits for a class of reversible quadratic vector field on R-3
(Journal of Mathematical Analysis and Applications, 2007-11-15) [Artigo]
For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite ...
Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
(Siam Journal on Applied Dynamical Systems, 2009-01-01) [Artigo]
In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular ...