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Journal articles
Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
Abstract : Consider in the phase space of classical mechanics a Radon measure that is a probability density carried by the graph of a Lipschitz continuous (or even less regular) vector field. We study the structure of the push-forward of such a measure by a Hamiltonian flow. In particular, we provide an estimate on the number of folds in the support of the transported measure that is the image of the initial graph by the flow. We also study in detail the type of singularities in the projection of the transported measure in configuration space (averaging out the momentum variable). We study the conditions under which this projected measure can have atoms, and give an example in which the projected measure is singular with respect to the Lebesgue measure and diffuse. We discuss applications of our results to the classical limit of the Schrödinger equation. Finally we present various examples and counterexamples showing that our results are sharp.
https://hal-polytechnique.archives-ouvertes.fr/hal-00706180
Contributor : François Golse <>
Submitted on : Friday, April 26, 2013 - 2:18:17 PM
Last modification on : Thursday, December 10, 2020 - 10:55:48 AM
Long-term archiving on: : Saturday, July 27, 2013 - 4:06:06 AM
Contributor : François Golse <>
Submitted on : Friday, April 26, 2013 - 2:18:17 PM
Last modification on : Thursday, December 10, 2020 - 10:55:48 AM
Long-term archiving on: : Saturday, July 27, 2013 - 4:06:06 AM
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