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Search: All articles in the CMB digital archive with keyword orbits

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1. CMB 2012 (vol 57 pp. 25)

Bourin, Jean-Christophe; Harada, Tetsuo; Lee, Eun-Young
 Subadditivity Inequalities for Compact Operators Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings. Keywords:concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalitiesCategories:47A63, 15A45

2. CMB 2011 (vol 54 pp. 693)

Lusala, Tsasa; Śniatycki, Jędrzej
 Stratified Subcartesian Spaces We show that if the family $\mathcal{O}$ of orbits of all vector fields on a subcartesian space $P$ is locally finite and each orbit in $\mathcal{O}$ is locally closed, then $\mathcal{O}$ defines a smooth Whitney A stratification of $P$. We also show that the stratification by orbit type of the space of orbits $M/G$ of a proper action of a Lie group $G$ on a smooth manifold $M$ is given by orbits of the family of all vector fields on $M/G$. Keywords:Subcartesian spaces, orbits of vector fields, stratifications, Whitney ConditionsCategories:58A40, 57N80

3. CMB 2011 (vol 54 pp. 311)

Marzougui, Habib
 Some Remarks Concerning the Topological Characterization of Limit Sets for Surface Flows We give some extension to theorems of JimÃ©nez LÃ³pez and Soler LÃ³pez concerning the topological characterization for limit sets of continuous flows on closed orientable surfaces. Keywords:flows on surfaces, orbits, class of an orbit, singularities, minimal set, limit set, regular cylinder Categories:37B20, 37E35

4. CMB 2007 (vol 50 pp. 447)

Śniatycki, Jędrzej
 Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces Let $\mathcal{F}$ be a family of vector fields on a manifold or a subcartesian space spanning a distribution $D$. We prove that an orbit $O$ of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$ and it has constant rank on $O$. This result implies Frobenius' theorem, and its various generalizations, on manifolds as well as on subcartesian spaces. Keywords:differential spaces, generalized distributions, orbits, Frobenius' theorem, Sussmann's theoremCategories:58A30, 58A40