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pro vyhledávání: '"Torres, David Martínez"'
We consider different phase spaces for the Toda flows and the less familiar SVD flows. For the Toda flow, we handle symmetric and non-symmetric matrices with real simple eigenvalues, possibly with a given profile. Profiles encode, for example, band m
Externí odkaz:
http://arxiv.org/abs/2302.07144
Autor:
Torres, David Martínez, Silva, Marcelo
We prove that a Poisson structure on a projective toric variety which is invariant by the torus action and whose symplectic leaves are the torus orbits is not exact. This is deduced from a geometric criterion for non-exactness of Poisson structures w
Externí odkaz:
http://arxiv.org/abs/2204.11916
Autor:
Torres, David Martínez
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first order prolongation of a family of second order PDEs. We describe explici
Externí odkaz:
http://arxiv.org/abs/2106.13080
We analyze \emph{submersions with Poisson fibres}. These are submersions whose total space carries a Poisson structure, on which the ambient Poisson structure pulls back, as a Dirac structure, to Poisson structures on each individual fibre. Our ``Poi
Externí odkaz:
http://arxiv.org/abs/2010.09058
Autor:
Torres, David Martínez
This paper describes two real analytic symplectomorphisms defined on appropriate dense open subsets of any coadjoint orbit of a compact semisimple Lie algebra. The first symplectomorphism sends the open dense subset to a bounded subset of a standard
Externí odkaz:
http://arxiv.org/abs/2001.02623
Autor:
Torres, David Martínez, Tomei, Carlos
We introduce an atlas adapted to the Toda flow on the manifold of full flags of any non-compact real semisimple Lie algebra, and on its Hessenberg-type submanifolds. In our local coordinates the Toda flow becomes linear. We use these new coordinates
Externí odkaz:
http://arxiv.org/abs/1909.02676
Let $G$ be a compact connected semisimple Lie group with Lie algebra $\mathfrak{g}$. Let $\mathcal{O}\subset\mathfrak{g}^*$ be a coadjoint orbit. The action of $G$ on $\mathcal{O}$ induces a morphism $\rho:G\to \mathrm{Homeo}(\mathcal{O})$. We prove
Externí odkaz:
http://arxiv.org/abs/1709.05247
Autor:
Torres, David Martínez, Miranda, Eva
Publikováno v:
Regul. Chaotic Dyn. 23 (2018), 1, 47-53
We prove that for regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group and we give some applications. In particular, we show that for regular unimodular Poisson manifolds top Poisson and foliated coh
Externí odkaz:
http://arxiv.org/abs/1709.01176
Autor:
Torres, David Martínez
We show that any proper Lie groupoid admits a compatible (real) analytic structure.
Comment: Introduction expanded. More detailed proofs included
Comment: Introduction expanded. More detailed proofs included
Externí odkaz:
http://arxiv.org/abs/1612.09012
Autor:
Torres, David Martínez, Miranda, Eva
Publikováno v:
J. Geom. Phys. 115 (2017), 131-138
In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamil
Externí odkaz:
http://arxiv.org/abs/1602.03542