QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition. © Springer-Verlag 1996.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Generic bifurcation of refracted systems

In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families of certain piecewise smooth vector fields named Refracted Systems. Such systems has a codimension-one submanifold as its discontinuity set. © 2012 Elsevier Ltd.

On singular foliations on the solid torus

We study smooth foliations on the solid torus S1×D2 having S1×{0} and S1×∂D2 as the only compact leaves and S1×{0} as singular set. We show that all other leaves can only be cylinders or planes, and give necessary conditions for the foliation to be a suspension of a diffeomorphism of the disc. © 2013 Elsevier B.V.

Estudo de ciclos limites em sistemas diferenciais lineares por partes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ciclos limites de campos de vetores polinomiais cúbicos e quadráticos

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

Campos de vetores lineares reversíveis equivariantes

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

Conjuntos limite e bifurfações de campos de vetores suaves por partes no plano

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

Análise global de sistemas quadráticos e cúbicos com duas circunferências não-concêntricas invariantes

Pós-graduação em Matematica Aplicada e Computacional - FCT

Estudo de conjuntos minimais para sistemas descontínuos em dimensões 2 e 3

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

Propriedades genéricas de sistemas hamiltonianos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conjuntos minimais de sistemas lineares por partes

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

Birth of limit cycles bifurcating from a nonsmooth center

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

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)