Zobrazeno 1 - 10
of 408
pro vyhledávání: '"34C07"'
Autor:
Buzzi, Claudio A., Novaes, Douglas D.
For a given natural number $n$, the second part of Hilbert's 16th Problem asks whether there exists a finite upper bound for the maximum number of limit cycles that planar polynomial vector fields of degree $n$ can have. This maximum number of limit
Externí odkaz:
http://arxiv.org/abs/2411.09594
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
The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five
Externí odkaz:
http://arxiv.org/abs/2405.10578
Autor:
Nascimento, F. J. S.
In this article it is proved that an analytical planar vector field with a non-degenerate center at $(0,0)$ is analytically conjugate, in a neighborhood of $(0,0)$, to a Hamiltonian vector field of the form $y\frac{\partial}{\partial x}-V'(x)\frac{\p
Externí odkaz:
http://arxiv.org/abs/2404.02036
In this paper, we generalize the Poincar\'e-Lyapunov method for systems with linear type centers to study nilpotent centers in switching polynomial systems and use it to investigate the bi-center problem of planar $Z_2$-equivariant cubic switching sy
Externí odkaz:
http://arxiv.org/abs/2403.05744
Autor:
Yeung, Melvin
We provide evidence that the approach of [Ilyashenko 1991] to the proof of Dulac's theorem has a gap. Although the asymptotics of [Ilyashenko 1991] capture far more than the asymptotics of Dulac, we prove that the arguments for why the asymptotics in
Externí odkaz:
http://arxiv.org/abs/2402.12506
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
We consider piecewise quadratic perturbations of centers of piecewise quadratic systems in two zones determined by a straight line through the origin. By means of expansions of the displacement map, we are able to find isolated zeros of it, without d
Externí odkaz:
http://arxiv.org/abs/2312.05847