We investigate the many-particle and mean-field correspondence for a non-Hermitian N-
particle Bose-Hubbard dimer where a complex on-site energy describes an effective decay …

We deal with polynomial vector fields of the form∑ dk= 1 P k (x 1,..., xd)∂/∂ xk with d⩾ 2.
Let mk be the degree of P k. We call (m 1,..., md) the degree of. We provide the best upper …

We investigate an open Bose–Hubbard dimer with a non-Hermitian term represents an
asymmetric coupling between the two sites. By mapping to the collective angular moment …

Let X be a homogeneous polynomial vector field of degree 2 on S^ 2. We show that if X has
at least a non-hyperbolic singularity, then it has no limit cycles. We give necessary and …

We consider the polynomial vector fields of arbitrary degree in\mathbb R^ 3 R 3 having the 2-
dimensional algebraic torus T^ 2 (l, m, n)={(x, y, z) ∈\mathbb R^ 3:(x^ 2l+ y^ 2m-r^ 2)^ 2+ z …

We study the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional
torus invariant by their flow. We characterize all the possible configurations of invariant …

First, we characterize all the polynomial vector fields in ℝ 4 which have the Clifford torus as
an invariant surface. Then we study the number of invariant meridians and parallels that …

In this paper, we characterize and study dynamical properties of cubic vector fields on the
sphere S 2={(x, y, z)∈ R 3| x 2+ y 2+ z 2= 1}. We start by classifying all degree three …

A class of reversible quadratic polynomial vector fields on S2 Page 1 J. Math. Anal. Appl. 371
(2010) 203–209 Contents lists available at ScienceDirect Journal of Mathematical Analysis …

The aim of this paper is the study of the center-focus and cyclicity problems inside the class
XX of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere …