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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 411, Pages 49–62 (Mi znsl5631)  
This article is cited in 4 scientific papers (total in 4 papers)

Amari–Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups

J. Lenellsa, G. Misiołekb

a Department of Mathematics, Baylor University, Waco, TX 76798, USA
b Department of Mathematics, University of Notre Dame, IN 46556, USA
Full-text PDF (250 kB) Citations (4)
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Abstract: We study the family of $\alpha$-connections of Amari–Chentsov on the homogeneous space $\mathcal D(M)/\mathcal D_\mu(M)$ of diffeomorphisms modulo volume-preserving diffeomorphims of a compact manifold $M$. We show that in some cases their geodesic equations yield completely integrable Hamiltonian systems.
Key words and phrases: diffeomorphism groups, Fisher–Rao metric, dual connections, integrable systems.
Received: 25.02.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 196, Issue 2, Pages 144–151
DOI: https://doi.org/10.1007/s10958-013-1646-5
Bibliographic databases:
Document Type: Article
UDC: 517.972+514.7+519.248
Language: English
Citation: J. Lenells, G. Misiołek, “Amari–Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 49–62; J. Math. Sci. (N. Y.), 196:2 (2014), 144–151
Citation in format AMSBIB
\Bibitem{LenMis13}
\by J.~Lenells, G.~Misio\l ek
\paper Amari--Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 411
\pages 49--62
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5631}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3048268}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 2
\pages 144--151
\crossref{https://doi.org/10.1007/s10958-013-1646-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897057450}
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  • https://www.mathnet.ru/eng/znsl/v411/p49
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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