We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight–homogeneous polynomial differential systems of weight–degree 2 with a center.

In this work, Liénard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated by computational methods. This puts in evidence that the homotopy analysis method is an useful tool to solve nonlinear differential equations.

The center problem for polynomial differential equations in the plane is one of the celebrated and longstanding problems in the qualitative theory of planar differential equations (see e.g. the works [Dulac, 1908], [Kapteyn, 1911], [Kapteyn, 1912], [Bautin, 1954], [Vulpe & Sibirskĭı, 1988], [Schlomiuk, 1993], [Żo la̧dek, 1994a] and [Żo la̧dek, 1994b]). It asks to distinguish a linear center betwe...

In this paper we study those cubic systems which are invariant under a rotation of 2π/4 radians. They are written as ż = εz + p z2z̄ − z̄3, where z is complex, the time is real, and ε = ε1+ iε2, p = p1+ ip2 are complex parameters. When they have some critical points at infinity, i.e. |p2| ≤ 1, it is well-known that they can have at most one (hyperbolic) limit cycle which surrounds the origin. On ...

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions fro...

Many nectar-feeding bird species decrease food intake when sugar concentration in food is increased. This feeding response can be explained by two alternative hypotheses: compensatory feeding and physiological constraint. The compensatory feeding hypothesis predicts that if birds vary intake to maintain a constant energy intake to match energy expenditures, then they should increase intake when...

In this article, it is shown that Riemann’s zeta function ζ(s) admits two limit representations when <(s) > 1. Each of these limit representations is deduced by using simple arguments based upon the classical Tannery’s (limiting) theorem for series.

In literature of Fourier transforms and Wavelet transforms, the basic space is L2(R). From the point of view of signal analysis, a signal f ∈ L2(R) can only be transient (or “wavelets”). During recent years in some application areas, it has become more common to motivate a theory via persistent rather than transient signals (e.g., [16, 28, 30, 42]). To work on persistent signals, people have to...

We show that the closure of compactly supported mapping class group an infinite type surface is not perfect and its abelianization contains a direct summand isomorphic to uncountable sum rationals. also extend this Torelli in case surfaces with genus indivisible copy free abelian as well. Finally we give application question automatic continuity by exhibiting discontinuous homomorphisms