35 citations · 76 across the 10 of their papers we have counts for
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On Gibbs states of mechanical systems with symmetries
Charles-Michel Marle
Gibbs states for the Hamiltonian action of a Lie group on a symplectic manifold were studied, and their possible applications in Physics and Cosmology were considered, by the Frenc…
The works of William Rowan Hamilton in geometrical optics and the Malus-Dupin theorem
Charles-Michel Marle
The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on tw…
From tools in symplectic and Poisson geometry to Souriau's theories of statistical mechanics and thermodynamics
Charles-Michel Marle
I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric mechanics and Mathematical Physics. After a short discussion of the…
Lie, symplectic and Poisson groupoids and their Lie algebroids
Charles-Michel Marle
Groupoids are mathematical structures able to describe symmetry properties more general than those described by groups. They were introduced (and named) by H. Brandt in 1926. Aroun…
The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
Charles-Michel Marle
Around 1923, Elie Cartan introduced affine connections on manifolds and definedthe main related concepts: torsion, curvature, holonomy groups. He discussed applications of these co…
Symmetries of Hamiltonian systems on symplectic and Poisson manifolds
Charles-Michel Marle
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentu…