Generic bifurcation of reversible vector fields on a 2-dimensional manifold

In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed

On the periodic solutions of a generalized smooth or non-smooth perturbed planar double pendulum

We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear planar double pendulum perturbed by smooth or non--smooth functions.Comment: arXiv admin note: substantial text overlap with arXiv:1109.637

Foliations, solvability and global injectivity

Let F: R^n -> R^n be a C^\infty map such that DF(x) is invertible for all x in R^n. We know that F is a local diffeomorphism but, in general, it is not globally injective. We discuss the relations between some additional hypothesis that guarantee the global injectivity of F. Further, based on one of these hypotheses, we establish a necessary condition for the existence of F: R^n -> R^n such that det DF = h, where h: R^n -> [0,\infty) is a given C^\infty function

Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals

Agraïments: The first author is partially supported by FEDER-UNAB-10-4E-378 and a CAPES grant 88881. 030454/2013-01 do Programa CSF-PVE

Limit cycles in Filippov systems having a circle as switching manifold

It is known that planar discontinuous piecewise linear differential systems separated by a straight line have no limit cycles when both linear differential systems are centers. Here, we study the limit cycles of the planar discontinuous piecewise linear differential systems separated by a circle when both linear differential systems are centers. Our main results show that such discontinuous piecewise differential systems can have zero, one, two, or three limit cycles, but no more limit cycles than three

On the Doubling Period Reversible Cusps in R3

We deal with normal forms of germs at the origin of reversible diffeomorphisms of the space whose lineae part is unipotent with two negative eigenvalues. The computing of these normal forms involves effective algebraic geometry algorithms. We also study generic one-paramater deformations