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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 3, Pages 537–556 (Mi izv1254)  

This article is cited in 16 scientific papers (total in 16 papers)

Polynomial integrals of Hamiltonian systems with exponential interaction

V. V. Kozlov, D. V. Treschev


Abstract: The problem on the complete integrability of Hamiltonian systems with exponential interaction is considered. These systems include, in particular, Toda chains and their generalizations. Conditions for the existence of a complete set of independent polynomial integrals are found. A complete classification of integrable systems is given by means of Dynkin diagrams. Certain new integrable chains are indicated.
Bibliography: 20 titles.

Full text: PDF file (2027 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:3, 555–574

Bibliographic databases:

UDC: 517.9+531.01
MSC: Primary 58F07, 58F05; Secondary 70H05, 34A25
Received: 15.06.1987

Citation: V. V. Kozlov, D. V. Treschev, “Polynomial integrals of Hamiltonian systems with exponential interaction”, Izv. Akad. Nauk SSSR Ser. Mat., 53:3 (1989), 537–556; Math. USSR-Izv., 34:3 (1990), 555–574

Citation in format AMSBIB
\Bibitem{KozTre89}
\by V.~V.~Kozlov, D.~V.~Treschev
\paper Polynomial integrals of Hamiltonian systems with exponential interaction
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 3
\pages 537--556
\mathnet{http://mi.mathnet.ru/izv1254}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1013711}
\zmath{https://zbmath.org/?q=an:0727.58018|0684.58012}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 3
\pages 555--574
\crossref{https://doi.org/10.1070/IM1990v034n03ABEH000670}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. L. Ziglin, “Polynomial first integrals of Hamiltonian systems with exponential interaction”, Funct. Anal. Appl., 25:3 (1991), 235–235  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Kozlov, N. V. Denisova, “Polynomial integrals of geodesic flows on a two-dimensional torus”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 469–481  mathnet  crossref  mathscinet  zmath  isi
    3. Harald Totland, “Integrable systems with Belavin-Drinfeld R-matrices”, Physics Letters A, 225:4-6 (1997), 263  crossref  elib
    4. K. V. Emel'yanov, “On the classification problem for Birkhoff integrable systems with potentials of exponential type”, Math. Notes, 67:5 (2000), 672–675  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. K. V. Emel'yanov, A. V. Tsygvintsev, “Kovalevskaya exponents of systems with exponential interaction”, Sb. Math., 191:10 (2000), 1459–1469  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Pantelis A Damianou, “On the bi-Hamiltonian structure of Bogoyavlensky–Toda lattices”, Nonlinearity, 17:2 (2004), 397  crossref  mathscinet  zmath  isi  elib
    7. V. V. Kozlov, D. V. Treschev, “Polynomial Conservation Laws in Quantum Systems”, Theoret. and Math. Phys., 140:3 (2004), 1283–1298  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Pantelis A. Damianou, Stelios P. Kouzaris, “Bogoyavlensky–Volterra and Birkhoff integrable systems”, Physica D: Nonlinear Phenomena, 195:1-2 (2004), 50  crossref
    9. PANTELIS A. DAMIANOU, “MULTIPLE HAMILTONIAN STRUCTURE OF BOGOYAVLENSKY–Toda LATTICES”, Rev. Math. Phys, 16:02 (2004), 175  crossref
    10. Vadim Kuznetsov, Evgeny Sklyanin, “Bäcklund Transformation for the BC-Type Toda Lattice”, SIGMA, 3 (2007), 080, 17 pp.  mathnet  crossref  mathscinet  zmath
    11. Vladimir D. Ivashchuk, Vitaly N. Melnikov, “On Brane Solutions Related to Non-Singular Kac–Moody Algebras”, SIGMA, 5 (2009), 070, 34 pp.  mathnet  crossref  mathscinet
    12. V. Rom-Kedar, D. Turaev, “Billiards: A singular perturbation limit of smooth Hamiltonian flows”, Chaos, 22:2 (2012), 026102  crossref
    13. Pantelis A. Damianou, Hervé Sabourin, Pol Vanhaecke, “Intermediate Toda Systems”, Regul. Chaotic Dyn., 20:3 (2015), 277–292  mathnet  crossref  mathscinet  zmath  adsnasa
    14. Thierry Combot, “Rational Integrability of Trigonometric Polynomial Potentials on the Flat Torus”, Regul. Chaotic Dyn., 22:4 (2017), 386–497  mathnet  crossref
    15. A. B. Shabat, V. E. Adler, “Cartan matrices in the Toda–Darboux chain theory”, Theoret. and Math. Phys., 196:1 (2018), 957–964  mathnet  crossref  crossref  adsnasa  isi  elib
    16. R. Ch. Kulaev, A. B. Shabat, “Conservation laws for Volterra chain with initial step-like condition”, Ufa Math. J., 11:1 (2019), 63–69  mathnet  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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