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First Order Hamiltonian Operators of Differential-Geometric Type in 2D

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Lie Theory and Its Applications in Physics (LT 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 191))

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Abstract

We present an alternative approach to the problem of classification of first order Hamiltonian operators of differential-geometric type in 2D.

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References

  1. B.A. Dubrovin and S.P. Novikov, Poisson brackets of hydrodynamic type, Dokl. Akad. Nauk SSSR 279 (1984), no. 2, 294–297.

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  4. E.V. Ferapontov, P. Lorenzoni and A. Savoldi, Hamiltonian Operators of Dubrovin-Novikov Type in 2D, Lett. Math. Phys. 105 (2015), 341–377.

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  5. A.V. Bolsinov, V.S. Matveev, Local normal forms for geodesically equivalent pseudo-Riemannian metrics, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6719–6749.

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Acknowledgements

We thank Jenya Ferapontov for useful discussions. P.L. is partially supported by the Italian MIUR Research Project Teorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite and by GNFM Progetto Giovani 2014 Aspetti geometrici e analitici dei sistemi integrabili.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, via Roberto Cozzi 53, 20125, Milano, Italy

    Paolo Lorenzoni

  2. Department of Mathematical Sciences, Loughborough University Leicestershire LE11 3TU, Loughborough, UK

    Andrea Savoldi

Authors
  1. Paolo Lorenzoni
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  2. Andrea Savoldi
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Corresponding author

Correspondence to Paolo Lorenzoni .

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Editors and Affiliations

  1. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Lorenzoni, P., Savoldi, A. (2016). First Order Hamiltonian Operators of Differential-Geometric Type in 2D. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_25

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