We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed
This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-know...
Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013.We st...
Altres ajuts: acord transformatiu CRUE-CSICWe solve the center-focus problem in a class of piecewise...
Abstract. We prove that there are one-parameter families of planar differential equations for which ...
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin ...
AbstractWe study the cyclicity and the center problem for a special family of planar differential eq...
Agraïments: The first author is supported by the NSF of China (No. 11201086, No.11401255) and the Ex...
AbstractIn this paper we consider analytic vector fields X0 having a non-degenerate center point e. ...
This dissertation is mainly a study of the center problem in the context of a family of three dimens...
AbstractFor real planar autonomous analytic differential equations we introduce the notion of persis...
In this paper we study the cyclicity of the centers of the quartic polynomial family written in comp...
The problem of distinguishing between a focus and a center is one of the classical problems in the q...
This note presents some advances regarding the Lyapunov constants of some families of planar polynom...
Agraïments: B. Fercec is supported by the Slovenian Research Agency; A.M. is partially supported by ...
We prove that any complex differential equation with two monomials of the form z˙ = azk ¯zl + bzm¯zn...
This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-know...
Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013.We st...
Altres ajuts: acord transformatiu CRUE-CSICWe solve the center-focus problem in a class of piecewise...
Abstract. We prove that there are one-parameter families of planar differential equations for which ...
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin ...
AbstractWe study the cyclicity and the center problem for a special family of planar differential eq...
Agraïments: The first author is supported by the NSF of China (No. 11201086, No.11401255) and the Ex...
AbstractIn this paper we consider analytic vector fields X0 having a non-degenerate center point e. ...
This dissertation is mainly a study of the center problem in the context of a family of three dimens...
AbstractFor real planar autonomous analytic differential equations we introduce the notion of persis...
In this paper we study the cyclicity of the centers of the quartic polynomial family written in comp...
The problem of distinguishing between a focus and a center is one of the classical problems in the q...
This note presents some advances regarding the Lyapunov constants of some families of planar polynom...
Agraïments: B. Fercec is supported by the Slovenian Research Agency; A.M. is partially supported by ...
We prove that any complex differential equation with two monomials of the form z˙ = azk ¯zl + bzm¯zn...
This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-know...
Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013.We st...
Altres ajuts: acord transformatiu CRUE-CSICWe solve the center-focus problem in a class of piecewise...
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