We consider a version of the Vlasov equation on the circle under a periodic potential V (x, t) and a repulsing smooth interaction W. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry–Mather theory and ideas of W. Gangbo, A. Tudorascu, and P. Bernard, we prove that, for any initial distribution of particles, it is possible to choose their initial speed so as to get a chaotic orbit on [0,+∞).
Bessi, U. (2012). Chaotic motions for a version of the Vlasov equation. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 44(4), 2496-2525.
Chaotic motions for a version of the Vlasov equation
BESSI, Ugo
2012-01-01
Abstract
We consider a version of the Vlasov equation on the circle under a periodic potential V (x, t) and a repulsing smooth interaction W. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry–Mather theory and ideas of W. Gangbo, A. Tudorascu, and P. Bernard, we prove that, for any initial distribution of particles, it is possible to choose their initial speed so as to get a chaotic orbit on [0,+∞).File in questo prodotto:
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