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pro vyhledávání: '"34C05"'
Autor:
García, Isaac A., Giné, Jaume
In this work we deal with analytic families of real planar vector fields $\mathcal{X}_\lambda$ having a monodromic singularity at the origin for any $\lambda \in \Lambda \subset \mathbb{R}^p$ and depending analytically on the parameters $\lambda$. Th
Externí odkaz:
http://arxiv.org/abs/2412.09197
Autor:
Llibre, J., Murza, Adrian C.
We extend to the $n$-dimensional ellipsoid contained in $\R^{n+1},$ the Darboux theory of integrability for polynomial vector fields in the $n$-dimensional sphere (Llibre et al., 2018). New results on the maximum number of invariant parallels and mer
Externí odkaz:
http://arxiv.org/abs/2410.21336
Autor:
Palma-Márquez, Jesús, Yeung, Melvin
We study large classes of real-valued analytic functions that naturally emerge in the understanding of Dulac's problem, which addresses the finiteness of limit cycles in planar differential equations. Building on a Maximum Modulus-type result we got,
Externí odkaz:
http://arxiv.org/abs/2410.07532
Autor:
von Bothmer, Hans-Christian
Let $\omega$ be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi homogeneous we give new conditions for existence of a Darboux integrating factor or a Darboux first integral. This is
Externí odkaz:
http://arxiv.org/abs/2409.01751
Autor:
Huang, Kaiyin, Liu, Weishi
In this work a dynamical system approach is taken to systematically investigate the one-dimensional classical Poisson-Boltzmann (PB) equation with various boundary conditions. This framework, particularly, the phase space portrait, has a unique advan
Externí odkaz:
http://arxiv.org/abs/2406.19696
Autor:
Abiev, Nurlan
Sets related to positively curved invariant Riemannian metrics on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the normalized Ricci flow equation. For Riemannian metrics of the Walla
Externí odkaz:
http://arxiv.org/abs/2402.11692
Autor:
Bueno, Antonio, Ortiz, Irene
Given $\lambda\in\mathbb{R}$ and $\textbf{v}\in\mathbb{L}^3$, a $\lambda$-translator with velocity $\textbf{v}$ is an immersed surface in $\mathbb{L}^3$ whose mean curvature satisfies $H=\langle N,\textbf{v}\rangle+\lambda$, where $N$ is a unit norma
Externí odkaz:
http://arxiv.org/abs/2402.07237
Let $\xi$ be a real analytic vector field with an elementary isolated singularity at $0\in \mathbb{R}^3$ and eigenvalues $\pm bi,c$ with $b,c\in \mathbb{R}$ and $b\neq 0$. We prove that all cycles of $\xi$ in a sufficiently small neighborhood of $0$,
Externí odkaz:
http://arxiv.org/abs/2401.16484
Publikováno v:
Phys. D 427 (2021), Paper No. 133017
Let $F\in\mathbb{C}[x,y]$ be a polynomial, $\gamma(z)\in \pi_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $\omega$ be a polynomial $1$-form, thus defining a polynomial deformation $dF+\epsilon\omega=0$ of the integrable foliati
Externí odkaz:
http://arxiv.org/abs/2401.05229
Given a function $\mathcal{H} \in C^1(\mathbb{S}^2)$, an $\mathcal{H}$-surface $\Sigma$ is a surface in the Euclidean space $\mathbb{R}^3$ whose mean curvature $H_\Sigma$ satisfies $H_\Sigma = \mathcal{H} \circ \eta$, where $\eta$ is the Gauss map of
Externí odkaz:
http://arxiv.org/abs/2401.04721