Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Oms, Cedric"'
In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key properties of es
Externí odkaz:
http://arxiv.org/abs/2310.19918
Publikováno v:
Regular and Chaotic Dynamics, 2023
In this short note, we prove that singular Reeb vector fields associated with generic $b$-contact forms have either (at least) $2N$ or an infinite number of escape orbits, where $N$ denotes the number of connected components of the critical set.
Externí odkaz:
http://arxiv.org/abs/2303.17690
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of $b^m$-symplectic manifolds. Novel techniques are introduced to associate smooth symplectic forms to the original
Externí odkaz:
http://arxiv.org/abs/2212.01344
Autor:
Cardona, Robert, Oms, Cédric
A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional leaves satis
Externí odkaz:
http://arxiv.org/abs/2207.12055
Autor:
Cardona, Robert, Oms, Cédric
Let $f$ be a Morse function on a closed surface $\Sigma$ such that zero is a regular value and such that $f$ admits neither positive minima nor negative maxima. In this expository note, we show that $\Sigma\times \mathbb{R}$ admits an $\mathbb{R}$-in
Externí odkaz:
http://arxiv.org/abs/2205.07503
Publikováno v:
In Advances in Mathematics December 2024 458 Part B
Publikováno v:
Communications in Contemporary Mathematics (2021) 2150076
Motivated by Poincar\'e's orbits going to infinity in the (restricted) three-body (see [26] and [6]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a $b$-contact form. This is done by using
Externí odkaz:
http://arxiv.org/abs/2010.00564
Autor:
Miranda, Eva, Oms, Cédric
Publikováno v:
Advances in Mathematics, Volume 389, 2021, 107925, ISSN 0001-8708
In this article, we investigate Reeb dynamics on $b^m$-contact manifolds, previously introduced in [MiO], which are contact away from a hypersurface $Z$ but satisfy certain transversality conditions on $Z$. The study of these contact structures is mo
Externí odkaz:
http://arxiv.org/abs/2005.09568
Autor:
Miranda, Eva, Oms, Cédric
In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular contact s
Externí odkaz:
http://arxiv.org/abs/1806.05638
Publikováno v:
Int. J. Geom. Methods Mod. Phys. 16 (2019), suppl. 1, 1940008, 16 pp
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure. At the end
Externí odkaz:
http://arxiv.org/abs/1705.03846