An explicit, computationally efficient, recursive formula is presented for computing the
normal form and center manifold of general n-dimensional systems associated with Hopf …

In this work, we study necessary and sufficient conditions for the existence of centers in two
families of linear centers with homogeneous quartic and quintic nonlinearities. Systems of …

This paper presents an explicit, computationally efficient, recursive formula for computing the
normal forms, center manifolds and nonlinear transformations for general n-dimensional …

Consider the two-dimensional autonomous systems of differential equations of the form...= P
[sub 3](x, y)+ P [sub 4](x, y),...=(Q [sub 3](x, y)+ Q [sub 4](x, y), where P [sub 3](x, y) and Q …

The paper deals with polynomials systems with degenerate infinity from different points of
view. We show the utility of the projective techniques for such systems, and a more detailed …

In this paper we study some aspects of the nondegenerate center problem for analytic and,
in particular, for polynomial vector fields. The relation between the existence of an inverse …

In this paper, we first present a survey of the known results on limit cycles and center
conditions for Liénard differential systems. Next we propose a generalization of such …

The computational problems which appear in the computation of the Poincaré–Liapunov
constants and the determination of their functionally independent number has led in recent …

In the last years many papers giving different methods to compute the Poincaré–Liapunov
constants have been published. In (Appl. Math. Warsaw 28 (2002) 17) a new method to …

We consider the class of polynomial differential equations ẋ= λx− y+ P n (x, y)+ P 2 n− 1 (x,
y), ẏ= x+ λy+ Q n (x, y)+ Q 2 n− 1 (x, y) with n≥ 2, where P i and Q i are homogeneous …