In this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our ...

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br ...

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br ...

A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the ...

We show that multiple polynomial ergodic averages arising from nilpo-tent groups of measure preserving transformations of a probability space always converge in the L 2 norm.

Neste trabalho veremos os retratos de fase, no disco de Poincaré, das formas normais locais das singularidades simétricas dos campos reversíveis do tipo (2; 0) e (2; 1) de baixa codimensão; uma aplicação da Teoria da Média ...

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our ...

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we ...