Some open problems in low dimensional dynamical systems
A Gasull - SeMA Journal, 2021 - Springer
The aim of this paper is to share with the mathematical community a list of 33 problems that I
have found along the years in my research. I believe that it is worth to think about them and …
have found along the years in my research. I believe that it is worth to think about them and …
[图书][B] Limit cycles of differential equations
C Christopher, C Li, J Torregrosa - 2007 - Springer
My aim in these notes is to consider some of the topics which surround the Poincaré center-
focus problem for polynomial systems. That is, given a polynomial system x= P (x, y), y= Q (x …
focus problem for polynomial systems. That is, given a polynomial system x= P (x, y), y= Q (x …
Critical periods in planar polynomial centers near a maximum number of cusps
P De Maesschalck, J Torregrosa - Journal of Differential Equations, 2024 - Elsevier
We provide the best lower bound for the number of critical periods of planar polynomial
centers known up to now. The new lower bound is obtained in the Hamiltonian class and …
centers known up to now. The new lower bound is obtained in the Hamiltonian class and …
The number of Kaplan-Yorke periodic solutions for delay differential equations
This paper is devoted to the number of Kaplan-Yorke periodic solutions (ie periodic
solutions with period 4) for the delay differential equation x˙(t)=− f (x (t− 1)), where f (x)= a x+ …
solutions with period 4) for the delay differential equation x˙(t)=− f (x (t− 1)), where f (x)= a x+ …
Criticality via first order development of the period constants
I Sánchez-Sánchez, J Torregrosa - Nonlinear Analysis, 2021 - Elsevier
In this work we study the criticality of some planar systems of polynomial differential
equations having a center for various low degrees n. To this end, we present a method …
equations having a center for various low degrees n. To this end, we present a method …
On the isochronous center of planar piecewise polynomial potential systems
C Liu, S Wang - Proceedings of the American Mathematical Society, 2022 - ams.org
This paper is devoted to the isochronicity of two kinds of planar piecewise polynomial
potential systems separated by $ x $-axis and $ y $-axis, respectively. By means of the …
potential systems separated by $ x $-axis and $ y $-axis, respectively. By means of the …
Study of Period Functions
L Chengzhi - Mathematical Theory and Applications, 2023 - mta.csu.edu.cn
In this survey article we first briefly introduce some concepts related to the period function of
a planar smooth (or analytic) vector field, and its isochronicity, monotonicity, and the number …
a planar smooth (or analytic) vector field, and its isochronicity, monotonicity, and the number …
The period function for some planar piecewise vector fields
MAS Santos - 2023 - repositorio.ufscar.br
In this work, we study the period function for fixed families of piecewise differential vector
fields with a line of discontinuities. These systems, indistinctly called piecewise or …
fields with a line of discontinuities. These systems, indistinctly called piecewise or …
Limit cycles and critical periods for some polynomial differential equations
I Sanchez Sanchez - 2021 - ddd.uab.cat
The present doctoral thesis is framed in the study of the center and cyclicity problems, as
well as isochronicity and criticality, in the context of the qualitative theory of differential …
well as isochronicity and criticality, in the context of the qualitative theory of differential …