Zobrazeno 1 - 10
of 407
pro vyhledávání: '"34C07"'
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
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
Nilpotent center conditions in cubic switching polynomial Li\'enard systems by higher-order analysis
The aim of this paper is to investigate two classical problems related to nilpotent center conditions and bifurcation of limit cycles in switching polynomial systems. Due to the difficulty in calculating the Lyapunov constants of switching polynomial
Externí odkaz:
http://arxiv.org/abs/2308.15102