Zobrazeno 1 - 10
of 5 766
pro vyhledávání: '"E. Hopf"'
Autor:
Corrêa, Maurício, Seade, José
In this expository article, we study and discuss invariants of vector fields and holomorphic foliations that intertwine the theories of complex analytic singular varieties and singular holomorphic foliations on complex manifolds: two different settin
Externí odkaz:
http://arxiv.org/abs/2411.12861
In this paper, we employ the framework of localization algebras to compute the equivariant K-homology class of the Euler characteristic operator, a central object in studying equivariant index theory on manifolds. This approach provides a powerful al
Externí odkaz:
http://arxiv.org/abs/2410.15103
Publikováno v:
Communications on Pure and Applied Analysis, 2024
The Poincar\'e-Hopf Theorem relates the Euler characteristic of a 2-dimensional compact manifold to the local behavior of smooth vector fields defined on it. However, despite the importance of Filippov vector fields, concerning both their theoretical
Externí odkaz:
http://arxiv.org/abs/2303.04316
Autor:
Barge, Héctor, Sanjurjo, José M. R.
In this paper we study the relationship of the Brouwer degree of a vector field with the dynamics of the induced flow. Analogous relations are studied for the index of a vector field. We obtain new forms of the Poincar% \'{e}-Hopf theorem and of the
Externí odkaz:
http://arxiv.org/abs/2303.06472
Equilibria analysis of a networked bivirus epidemic model using Poincar\'e--Hopf and Manifold Theory
Autor:
Anderson, Brian D. O., Ye, Mengbin
Publikováno v:
SIAM Journal of Applied Dynamical Systems, 22 (4): pp. 2856 - 2889, 2023
This paper considers a deterministic Susceptible-Infected-Susceptible (SIS) networked bivirus epidemic model (termed the bivirus model for short), in which two competing viruses spread through a set of populations (nodes) connected by two graphs, whi
Externí odkaz:
http://arxiv.org/abs/2210.11044
It is well known in the literature that the momentum space associated to the $\kappa$-Poincar\'e algebra is described by the Lie group $\mathsf{A}\mathsf{N}(3)$. In this letter we show that the full $\kappa$-Poincar\'e Hopf algebra structure can be o
Externí odkaz:
http://arxiv.org/abs/2204.09394
Autor:
Pim, Aaron
The Poincar\'e-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs real-analytic vector fields, which are tangential to surfaces with smo
Externí odkaz:
http://arxiv.org/abs/2106.01447
Autor:
Kvalheim, Matthew D.
A generalization of the Poincar\'{e}-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct "modes" are not assumed to have constant dimension; and r
Externí odkaz:
http://arxiv.org/abs/2108.07434
Autor:
Rau, Johannes
Publikováno v:
Journal of Combinatorial Theory, Series A, Volume 196, 2023, 105733
We express the beta invariant of a loopless matroid as tropical self-intersection number of the diagonal of its matroid fan (a "local" Poincar\'e-Hopf theorem). This provides another example of uncovering the "geometry" of matroids by expressing thei
Externí odkaz:
http://arxiv.org/abs/2007.11642
Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated determinantal singularities and $\omega$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense). Under some technical conditions on $r$ we use two gen
Externí odkaz:
http://arxiv.org/abs/2007.05026