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Amari–Chentsov Connections and their Geodesics on Homogeneous Spaces of Diffeomorphism Groups

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We study the family of Amari–Chentsov α-connections on the homogeneous space \( {{{\mathcal{D}(M)}} \left/ {{{{\mathcal{D}}_{\mu }}(M)}} \right.} \) of diffeomorphisms modulo volume-preserving diffeomorphisms of a compact manifold M. We show that in some cases their geodesic equations yield completely integrable Hamiltonian systems. Bibliography: 10 titles.

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Authors and Affiliations

  1. Department of Mathematics, Baylor University, Waco, USA

    J. Lenells

  2. Department of Mathematics, University of Notre Dame, Notre Dame, USA

    G. Misiołek

Authors
  1. J. Lenells
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  2. G. Misiołek
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Correspondence to J. Lenells.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 411, 2013, pp. 49–62.

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Lenells, J., Misiołek, G. Amari–Chentsov Connections and their Geodesics on Homogeneous Spaces of Diffeomorphism Groups. J Math Sci 196, 144–151 (2014). https://doi.org/10.1007/s10958-013-1646-5

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  • DOI: https://doi.org/10.1007/s10958-013-1646-5

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