Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Ayuso, P. Fortuny"'
Autor:
Cano, J., Ayuso, P. Fortuny
Given a differential or $q$-difference equation $P$ of order $n$, we prove that the set of exponents of a generalized power series solution has its rational rank bounded by the rational rank of the support of $P$ plus $n$. We also prove that when the
Externí odkaz:
http://arxiv.org/abs/2406.06115
Autor:
Ayuso, Pedro Fortuny, Ribón, Javier
We show that there is a basis of the set of K\"{a}hler differentials of an irreducible germ of holomorphic plane curve whose non-trivial elements correspond to dicritical foliations. Indeed, we discuss several concepts of generation for the semimodul
Externí odkaz:
http://arxiv.org/abs/2405.13958
Autor:
Ayuso, Pedro Fortuny, Ribón, Javier
Let ${\mathcal C}$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the ${\mathbb C}[[x]]$-module of K\"ahler differentials for generic $\Gamma \in {\mathcal C}$, algorithmically, and study
Externí odkaz:
http://arxiv.org/abs/2405.09684
Complexity of Puiseux solutions of differential and $q$-difference equations of order and degree one
We relate the complexity of both differential and $q$-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too. In this spirit, w
Externí odkaz:
http://arxiv.org/abs/2310.15409
Autor:
Ayuso, Pedro Fortuny, Ribón, Javier
We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are isolated, i.e.
Externí odkaz:
http://arxiv.org/abs/2310.13131
We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated to the Euler equation, and the initial/final and/or
Externí odkaz:
http://arxiv.org/abs/2301.09886
Autor:
Ayuso, Pedro Fortuny
Using vector fields we obtain an irreducibility criterion for hypersurfaces. It only requires the Weierstrass division.
Comment: ***IMPORTANT***: the paper is wrong. I am leaving it here because it may be enlightening for someone with more insig
Comment: ***IMPORTANT***: the paper is wrong. I am leaving it here because it may be enlightening for someone with more insig
Externí odkaz:
http://arxiv.org/abs/2106.01163
Autor:
Ayuso, Pedro Fortuny
We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.
Comment: The paper is obviously wrong, it conflates one concept with another. Apologies to all the readers
Comment: The paper is obviously wrong, it conflates one concept with another. Apologies to all the readers
Externí odkaz:
http://arxiv.org/abs/2106.00562
Autor:
Ayuso, Pedro Fortuny
We prove that two analytic branches in $(\mathbb{C}^n,0)$ whose dual resolution graph is the same admit an ambient isotopy which is smooth outside the origin. A weaker version of the converse is also proved.
Externí odkaz:
http://arxiv.org/abs/2105.13107
Publikováno v:
Rev. Mat. Iberoam. 37 (2021), no. 6, pp. 2229-2244
Let ${\mathcal F}$ be a germ of holomorphic foliation defined in a neighborhood of the origin of ${\mathbb C}^{2}$ that has a germ of irreducible holomorphic invariant curve $\gamma$. We provide a lower bound for the vanishing multiplicity of ${\math
Externí odkaz:
http://arxiv.org/abs/2007.04757