Results 1 to 10 of about 178 (165)
Nonlinear flag manifolds as coadjoint orbits [PDF]
Annals of Global Analysis and Geometry, 2020 AbstractA nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e ...
Cornelia Vizman +2 more
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Noise and Dissipation on Coadjoint Orbits. [PDF]
J Nonlinear Sci, 2018 We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random attractors are found for this general class of systems when the Lie algebra is semi- simple, provided the top Lyapunov ...
Arnaudon A, De Castro AL, Holm DD.
europepmc +7 more sources
Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation [PDF]
Entropy, 2022 The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action.
Frédéric Barbaresco
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Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics [PDF]
Entropy, 2020 In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau’s symplectic model of statistical ...
Frédéric Barbaresco +1 more
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Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]
EntropyThe explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
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Adjoint and Coadjoint Orbits of the Poincaré Group [PDF]
Acta Applicandae Mathematicae, 2006 Revised arguments in section 6, results unchanged.
Richard Cushman, Cushman Richard
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Involutions in S n and associated coadjoint orbits
Journal of Mathematical Sciences, 2008 In the paper we study the coadjoint orbits of the group $\mathrm{UT}(n,K)$ associated with involutions. We obtain a formula for dimension of the orbit. We construct a polarization for the canonical element of orbit. We find a system of generators in the defining ideal of orbit.
Panov A N, A N Panov
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Ruang Fase Tereduksi Grup Lie Aff (1)
Jambura Journal of Mathematics, 2021 ABSTRAK Dalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang ...
Edi Kurniadi
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Coadjoint semi-direct orbits and Lagrangian families with respect to Hermitian form
Revista Integración, 2023 We use the underlying structure of then coadjoint orbits of a semidirect product of a connected Lie group and a vector space to obtain families of Lagrangian submanifolds in the adjoint orbits of complex semisimple Lie groups with respect to the ...
Jhoan Báez, Luiz A.B. San Martin
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Leaves of stacky Lie algebroids
Comptes Rendus. Mathématique, 2020 We show that the leaves of an LA-groupoid which pass through the unit manifold are, modulo a connectedness issue, Lie groupoids. We illustrate this phenomenon by considering the cotangent Lie algebroids of Poisson groupoids thus obtaining an interesting ...
Álvarez, Daniel
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