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CMFD, 2011, Volume 42, Pages 48–61 (Mi cmfd189)  

This article is cited in 2 scientific papers (total in 2 papers)

Hypoelliptic heat kernel over $3$-step nilpotent Lie groups

U. Boscaina, J.-P. Gauthierb, F. Rossic

a CMAP, École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex, France
b Laboratoire LSIS, Université de Toulon, France
c Laboratoire LSIS, Université Paul Cézanne, Marseille, France

Abstract: In this paper, we provide explicitly the connection between the hypoelliptic heat kernel for some $3$-step sub-Riemannian manifolds and the quartic oscillator. We study the left-invariant sub-Riemannian structure on two nilpotent Lie groups, namely, the (2,3,4) group (called the Engel group) and the (2,3,5) group (called the Cartan group or the generalized Dido problem). Our main technique is noncommutative Fourier analysis, which permits us to transform the hypoelliptic heat equation into a one-dimensional heat equation with a quartic potential.

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English version:
Journal of Mathematical Sciences, 2014, 199:6, 614–628

Bibliographic databases:

Document Type: Article
UDC: 517.938

Citation: U. Boscain, J.-P. Gauthier, F. Rossi, “Hypoelliptic heat kernel over $3$-step nilpotent Lie groups”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 48–61; Journal of Mathematical Sciences, 199:6 (2014), 614–628

Citation in format AMSBIB
\Bibitem{BosGauRos11}
\by U.~Boscain, J.-P.~Gauthier, F.~Rossi
\paper Hypoelliptic heat kernel over $3$-step nilpotent Lie groups
\inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009)
\serial CMFD
\yr 2011
\vol 42
\pages 48--61
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013827}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 199
\issue 6
\pages 614--628
\crossref{https://doi.org/10.1007/s10958-014-1889-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902766595}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Biagi S., Bonfiglioli A., “The Existence of a Global Fundamental Solution For Homogeneous Hormander Operators Via a Global Lifting Method”, Proc. London Math. Soc., 114:5 (2017), 855–889  crossref  mathscinet  zmath  isi  scopus
    2. M. V. Kuznetsov, “Absence of nontrivial symmetries to the heat equation in Goursat groups of dimension at least $4$”, Siberian Math. J., 60:1 (2019), 108–113  mathnet  crossref  crossref  isi
  • Современная математика. Фундаментальные направления
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