Displaying similar documents to “Semi-algebraic neighborhoods of closed semi-algebraic sets”

Homology classes of real algebraic sets

Wojciech Kucharz (2008)

Annales de l’institut Fourier

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There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.

Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula

Frédéric Faure (2007)

Annales de l’institut Fourier

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We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator M ^ . The usual semi-classical Trace formula expresses T r M ^ t for finite time t , in the limit ℏ → 0 , in terms of periodic orbits of M of period t . Recent work reach time t ≪ t E / 6 where t E = log ( 1 / ℏ ) / λ is the Ehrenfest time, and λ is the Lyapounov coefficient. Using a semi-classical...