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pro vyhledávání: '"LLibre, Jaume"'
Autor:
Llibre, Jaume, Santana, Paulo
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic dynamics.
Externí odkaz:
http://arxiv.org/abs/2407.05151
Autor:
da Cruz, Leonardo P. C., LLibre, Jaume
A center of a differential system in the plane $\mathbb{R}^2$ is an equilibrium point $p$ having a neighborhood $U$ such that $U\setminus \{p\}$ is filled of periodic orbits. A center $p$ is global when $\mathbb{R}^2\setminus \{p\}$ is filled of peri
Externí odkaz:
http://arxiv.org/abs/2312.05709
Autor:
Llibre, Jaume, Rondón, Gabriel
A difficult classical problem in the qualitative theory of differential systems in the plane $\mathbb{R}^2$ is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of
Externí odkaz:
http://arxiv.org/abs/2310.07454
Publikováno v:
Chaos, 2023
The generalized Chazy differential equation corresponds to the following two-parameter family of differential equations \begin{equation*}\label{gcdeq} \dddot x+|x|^q \ddot x+\dfrac{k |x|^q}{x}\dot x^2=0, \end{equation*} which has its regularity varyi
Externí odkaz:
http://arxiv.org/abs/2307.00087
Autor:
Cufí-Cabré, Clara, Llibre, Jaume
Publikováno v:
Pacific J. Math. 324 (2023) 249-263
It is well known that linear vector fields defined in $\mathbb{R}^n$ can not have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of perio
Externí odkaz:
http://arxiv.org/abs/2207.07006
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of these syst
Externí odkaz:
http://arxiv.org/abs/2205.04554