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Ergodic averages and free 2 actions

Zoltán Buczolich (1999)

Fundamenta Mathematicae

If the ergodic transformations S, T generate a free 2 action on a finite non-atomic measure space (X,S,µ) then for any c 1 , c 2 there exists a measurable function f on X for which ( N + 1 ) - 1 j = 0 N f ( S j x ) c 1 and ( N + 1 ) - 1 j = 0 N f ( T j x ) c 2 µ -almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.

Generalized PN manifolds and separation of variables

Fernand Pelletier, Patrick Cabau (2008)

Banach Center Publications

The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.

Geometric quantization and no-go theorems

Viktor Ginzburg, Richard Montgomery (2000)

Banach Center Publications

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a...

Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.

A. López Almorox, C. Tejero Prieto (2001)

RACSAM

Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.

Hierarchy of integrable geodesic flows.

Peter Topalov (2000)

Publicacions Matemàtiques

A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.

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