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pro vyhledávání: '"ALARCÓN, BEGOÑA"'
This is a complete study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a contracting homogeneous polynomial. The contracting nonlinearity provides the existence of an in
Externí odkaz:
http://arxiv.org/abs/2307.16020
This is a complete study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a homogeneous polynomial. It extends previous work by other authors that was mainly concerned with
Externí odkaz:
http://arxiv.org/abs/2106.07516
Akademický článek
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We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of $D_2$-symmetric maps, f
Externí odkaz:
http://arxiv.org/abs/1605.08000
Autor:
Alarcón, Begoña, Rabanal, Roland
We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolated singular points on the plane, and the initial families are obtained
Externí odkaz:
http://arxiv.org/abs/1503.07617
We probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivarian
Externí odkaz:
http://arxiv.org/abs/1110.2710
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element
Externí odkaz:
http://arxiv.org/abs/0706.2580
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
Externí odkaz:
http://arxiv.org/abs/math/0703466
Autor:
ALARCÓN, BEGOÑA, RABANAL, ROLAND
Publikováno v:
Proceedings of the American Mathematical Society, 2017 Jul 01. 145(7), 3033-3046.
Externí odkaz:
https://www.jstor.org/stable/90006385
Publikováno v:
In Indagationes Mathematicae September 2012 23(3):603-608