The Experts below are selected from a list of 2916 Experts worldwide ranked by ideXlab platform
Luiz A. B. San Martin - One of the best experts on this subject based on the ideXlab platform.
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Control systems on flag manifolds and their chain control sets
Discrete and Continuous Dynamical Systems, 2017Co-Authors: Víctor Ayala, Adriano Da Silva, Luiz A. B. San MartinAbstract:A right-invariant control system \begin{document}$Σ$\end{document} on a connected Lie group \begin{document}$G$\end{document} induce affine control systems \begin{document}$Σ_{Θ}$\end{document} on every flag manifold \begin{document}$\mathbb{F}_{Θ}=G/P_{Θ}$\end{document} . In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with Nonempty Interior and, if the number of the control sets with Nonempty Interior coincides with the number of the chain control sets, then the closure of any control set with Nonempty Interior is a chain control set. Some relevant examples are included.
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Control Systems on Flag Manifolds and their chain Control sets
arXiv: Dynamical Systems, 2016Co-Authors: Víctor Ayala, Adriano Da Silva, Luiz A. B. San MartinAbstract:In this paper we shown that the chain control sets of induced systems on flag manifolds coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with Nonempty Interior and, if the number of the control sets with Nonempty Interior coincides with the number of the chain control sets, then the closure of any control set with Nonempty Interior is a chain control set.
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Semigroups in symmetric Lie groups
Indagationes Mathematicae, 2007Co-Authors: Laércio J. Dossantos, Luiz A. B. San MartinAbstract:Let G be a connected noncompact semi-simple real Lie group, an involutive automorphism of G, and L a subgroup of G such that G 0 L G . In this article we give conditions on x 2 G such that the semigroup generated by the coset Lx has Nonempty Interior in G. As a consequence we prove that for several the fixed point group G is a maximal semigroup.
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The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups
Monatshefte für Mathematik, 2002Co-Authors: Luiz A. B. San Martin, Alexandre J. SantanaAbstract:Let G be a noncompact semi-simple Lie group and \(\) a Lie semigroup with Nonempty Interior. We study the homotopy groups \(\), \(\), of S. Generalizing a well known fact for G, it is proved that there exists a compact and connected subgroup \(\) such that \(\) is isomorphic to \(\). Furthermore, there exists a coset \(\)z contained in int S which is a deformation retract of S.
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Maximal semigroups in semi-simple Lie groups
Transactions of the American Mathematical Society, 2001Co-Authors: Luiz A. B. San MartinAbstract:The maximal semigroups with Nonempty Interior in a semi-simple Lie group with finite' center are characterized as compression semigroups of subsets in the flag manifolds of the group. For this purpose a convexity theory, called here B-convexity, based on the open Bruhat cells is developed. It turns out that a semigroup with Nonempty Interior is maximal if and only if it is the compression semigroup of the Interior of a B-convex set.
Alexandre J. Santana - One of the best experts on this subject based on the ideXlab platform.
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Bounds for Invariance Pressure
arXiv: Optimization and Control, 2019Co-Authors: Fritz Colonius, Alexandre J. Santana, João A. N. CossichAbstract:This paper provides an upper for the invariance pressure of control sets with Nonempty Interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.
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Semigroups of Affine Groups, Controllability of Affine Systems and Affine Bilinear Systems in $\mathrm{Sl}(2,\mathbb{R})\rtimes\mathbb{R}^{2}$
Siam Journal on Control and Optimization, 2009Co-Authors: Osvaldo Germano Do Rocio, Alexandre J. Santana, Marcos A. VerdiAbstract:Let $G=B\rtimes V$ be an affine group given by a semidirect product of connected Lie group $B$ and vector space $V$, where $B$ has a transitive representation on $V$. We study semigroups of $G$ with Nonempty Interior. As an application, we obtain a characterization of controllability of bilinear systems in the case of $\mathrm{Sl}(2,\mathbb{R})\rtimes\mathbb{R}^{2}$.
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Invariant Cones for Semigroups in Transitive Lie Groups
Journal of Dynamical and Control Systems, 2008Co-Authors: O. G. Do Rocio, L. A. Martin, Alexandre J. SantanaAbstract:Let G be a connected Lie group which has a transitive representation on $ \mathbb{R}^{ n } $ and S ? G be a semigroup with a Nonempty Interior. We study necessary and sufficient conditions for the existence of the S-invariant pointed and generating cone W ? $ \mathbb{R}^{ n } $ , where the parabolic type of S arises as a central concept.
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The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups
Monatshefte für Mathematik, 2002Co-Authors: Luiz A. B. San Martin, Alexandre J. SantanaAbstract:Let G be a noncompact semi-simple Lie group and \(\) a Lie semigroup with Nonempty Interior. We study the homotopy groups \(\), \(\), of S. Generalizing a well known fact for G, it is proved that there exists a compact and connected subgroup \(\) such that \(\) is isomorphic to \(\). Furthermore, there exists a coset \(\)z contained in int S which is a deformation retract of S.
Małgorzata Terepeta - One of the best experts on this subject based on the ideXlab platform.
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On similarity between topologies
Open Mathematics, 2014Co-Authors: Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata TerepetaAbstract:Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have Nonempty Interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
Ying Xiong - One of the best experts on this subject based on the ideXlab platform.
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self similarity positive lebesgue measure and Nonempty Interior
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Ying XiongAbstract:Abstract In this paper, we introduce BBI spaces (“big balls of itself”), which based on the notion of BPI spaces (“big pieces of itself”) used by David and Semmes to study self-similarity. We prove that the “self-similar” construction described by BBI spaces ensures the equivalence of positive Lebesgue measure and Nonempty Interior. We apply this result to self-conformal sets satisfying the WSC and prove that positive Lebesgue measure implies Nonempty Interior for such sets. This generalizes Zerner's corresponding result for self-similar sets.
Artur Bartoszewicz - One of the best experts on this subject based on the ideXlab platform.
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On similarity between topologies
Open Mathematics, 2014Co-Authors: Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata TerepetaAbstract:Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have Nonempty Interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
