Zobrazeno 1 - 10
of 2 599
pro vyhledávání: '"Gasull, A."'
Autor:
Gasull, Armengol, Rojas, David
We prove that the period function of the center at the origin of the $\mathbb{Z}_k$-equivariant differential equation $\dot{z}=iz+a(z\overline{z})^nz^{k+1}, a\ne0,$ is monotonous decreasing for all $n$ and $k$ positive integers, solving a conjecture
Externí odkaz:
http://arxiv.org/abs/2411.12408
This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve $(4x^2-1)(4y^2-1)=0.$ The main interest for this type of vector fields comes from their appearan
Externí odkaz:
http://arxiv.org/abs/2410.15354
We consider the family of piecewise linear maps $$F_{a,b}(x,y)=\left(|x| - y + a, x - |y| + b\right),$$ where $(a,b)\in \mathbb{R}^2$. This family belongs to a wider one that has deserved some interest in the recent years as it provides a framework f
Externí odkaz:
http://arxiv.org/abs/2410.01052
Let $X$ be a planar smooth vector field with a polycycle $\Gamma^n$ with $n$ sides and all its corners, that are at most $n$ singularities, being hyperbolic saddles. In this paper we study the cyclicity of $\Gamma^n$ in terms of the hyperbolicity rat
Externí odkaz:
http://arxiv.org/abs/2407.20721
Autor:
Gasull, Armengol, Santana, Paulo
Let $\mathcal{H}(n)$ be the maximum number of limit cycles that a planar polynomial vector field of degree $n$ can have. In this paper we prove that $\mathcal{H}(n)$ is realizable by structurally stable vector fields with only hyperbolic limit cycles
Externí odkaz:
http://arxiv.org/abs/2407.13465
Autor:
Gasull, Armengol, Santana, Paulo
We study the number of limit cycles that a planar polynomial vector field can have as a function of its number $m$ of monomials. We prove that the number of limit cycles increases at least quadratically with $m$ and we provide good lower bounds for $
Externí odkaz:
http://arxiv.org/abs/2405.04281
In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view: study of the number
Externí odkaz:
http://arxiv.org/abs/2312.01452
We study the dynamics of the piecewise planar rotations $F_{\lambda}(z)=\lambda (z-H(z)), $ with $z\in\C$, $H(z)=1$ if $\mathrm{Im}(z)\ge0,$ $H(z)=-1$ if $\mathrm{Im}(z)<0,$ and $\lambda=\mathrm{e}^{i \alpha} \in\C$, being $\alpha$ a rational multipl
Externí odkaz:
http://arxiv.org/abs/2306.17543
Publikováno v:
Signal Transduction and Targeted Therapy, Vol 9, Iss 1, Pp 1-3 (2024)
Externí odkaz:
https://doaj.org/article/0060757100ba43568e06666c7ec6a7c8
We study three questions related to Machin's type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated $2$-integers, that is values of the form $b/2^a$ for some integers $a$ and~$b$. These formulas
Externí odkaz:
http://arxiv.org/abs/2302.00154