Two-Valued Groups, Kummer Varieties, and Integrable Billiards

Arnol’d, V.: Mathematical methods of classical mechanics. Springer, New York (1978)

Audin, M.: Spinning tops. An introduction to integrable systems, Cambridge studies in advanced mathematics 51 (1999)

Audin, M.: Courbes algebriques et syst‘emes integrables: geodesiques des quadriques. Expo. Math. 12, 193–226 (1994)

Baker, H.F.: On the hyperelliptic sigma functions, Am. J. Math. 301–384 (1898)

Buchstaber, V.M., Novikov, S.P.: Formal groups, power systems and Adams operators. Mat. Sb. (N. S) 84(126), 81–118 (1971). (in Russian)

Buchstaber, V.M., Rees, E.G.: Multivalued groups, their representations and Hopf algebras. Transform. Groups 2, 325–249 (1997)

Buchstaber, V.M., Veselov, A.P.: Integrable correspondences and algebraic representations of multivalued groups, Internat. Math. Res. Notices, 381–400 (1996)

Buchstaber, V.M.: Functional equations that are associated with addition theorems for elliptic functions, and two valued groups, Uspekhi Math. Nauk 45 (1990) No 3 (273) 185–186 (Russian) English translation. Russian Math. Surveys 45(3), 213–215 (1990)

Buchstaber, V.M.: n-Valued groups: theory and applications. Moscow Math. J. 6, 57–84 (2006)

Buchstaber, V.M.: Polynomial dynamical systems and the Korteweg-de Vries equation. Proc. Steklov Inst. Math. 294, 176–200 (2016)

Buchstaber, V.M., Mikhailov, A.V.: Infinite-dimensional lie algebras determined by the space of symmetric squares of hyperelliptic curves. Funct. Anal. Appl. 51(1), 4–27 (2017)

Buchstaber, V.M., Enolskii, V.Z., Leikin, D.V.: Kleinian functions, hyperelliptic Jacobians and applications., Reviews in Mathematics and Math. Physics, Krichever, I.M., Novikov, S.P. Editors, v. 10, part 2, Gordon and Breach, London, 3–120 (1997)

Buchstaber, V.M., Enolskii, V.Z., Leikin, D.V.: Multi-dimensional sigma-functions. arXiv:1208.0990 [math-ph] (2012)

Buchstaber, V.M., Leykin, D.V.: Addition laws on Jacobian varieties of plane algebraic curves. Proc. Steklov Math. Inst. 251(4), 49–120 (2005)

Buchstaber, V.M., Rees, E.G.: The Gelfand map and symmetric products. Selecta Math. (N.S.) 8(4), 523–535 (2002)

Darboux, G.: Principes de géométrie analytique, p. 519. Gauthier-Villars, Paris (1917)

Donagi, R.: Group law on the intersection of two quadrics Ann. Sc. Norm. Sup. Pisa, 217–239 (1980)

Dragović, V.: Poncelet-Darboux curves, their complete decomposition and Marden theorem. Internat. Math. Res. Notes 2011, 3502–3523 (2011)

Dragović, V.: Multi-valued hyperelliptic continous fractions of generalized Halphen type. Internat. Math. Res. Notices 2009, 1891–1932 (2009)

Dragović, V.: Generalization and Geometrization of the Kowalevski top. Comm. Math. Phys. 298(1), 37–64 (2010)

Dragović, V., Kukić, K.: Discriminantly separable polynomials and quad-graphs. J. Geom. Mech. 6(3), 319–333 (2014)

Dragović, V., Kukić, K.: Systems of the Kowalevski type and discriminantly separable polynomials. Regul. Chaotic Dyn. 19(2), 162–184 (2014)

Dragović, V., Kukić, K.: The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta-functions via discriminantly separable polynomials. Proc. Steklov Math. Inst. 286, 224–239 (2014)

Dragović, V., Radnović, M.: Geometry of integrable billiards and pencils of quadrics. J. Math. Pures Appl. 85, 758–790 (2006)

Dragović, V., Radnović, M.: Hyperelliptic Jacobians as Billiard Algebra of Pencils of Quadrics: Beyond Poncelet Porisms. Adv. Math. 219, 1577–1607 (2008)

Dragović, V., Radnović, M.: Poncelet porisms and beyond: integrable billiards, hyperelliptic Jacobians and pencils of quadrics, Frontiers in Mathematics, Birkhauser/Springer, 294, ISBN 978-3-0348-0014-3 (2011)

Dragović, V., Radnović, M.: Bicentennial of the Great Poncelet Theorem. Bull. Am. Math. Soc. 51, 373–445 (2014)

Dragović, V., Radnović, M.: Pseudo-integrable billiards and arithemetic dynamics. J. Modern Dyn. 8(1), 109–132 (2014)

Dragović, V., Radnović, M.: Periods of pseudo-integrable billiards. Arnold Math. J. 1(1), 69–73 (2015). https://doi.org/10.1007/s40598-014-0004-0

Dragović, V., Radnović, M.: Pseudo-integrable billiards and double reflection nets. Russian Math. Surv. 70(1), 3–34 (2015). https://doi.org/10.4213/rm9648

Dragović, V., Gajić, B.: Some recent generalizations of the classical rigid body systems. Arnold Math. J. 2(4), 511–578 (2016)

Dubrovin, B.A., Novikov, S.P.: A periodic problem for the Korteweg-de Vries and Sturm-Liouville equations. Their connection with algebraic geometry (Russian) Dokl. Akad. Nauk SSSR 219 (1974), 531-534, English translation: Soviet Math. Dokl. 15 (1974), no. 6, 1597–1601 (1975)

Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V.: Discriminants, resultants and multidimensional deteminants. Birhauser, Boston (1994)

Golubev, V.V.: Lectures on the integration of motion of a heavy rigid body around a fixed point, Gostechizdat, Moscow, 1953 [in Russian] Israel program for scintific literature, English translation (1960)

Griffiths, Ph, Harris, J.: Principles of Algebraic Geometry. Wiley Classics library edition (1994)

Knörrer, H.: Geodesics on the ellipsoid. Invent. Math. 59, 119–143 (1980)

Kowalevski, S.: Sur la probleme de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12, 177–232 (1889)

Moser, J., Veselov, A.: Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139(2), 217–243 (1991)

Narasimhan, M., Ramanan, S.: Moduli of vector bundles on compact Riemann surfaces. Ann. Math. 2(89), 14–51 (1969)

Tyurin, A.N.: On intersection of quadrics. Russian Math. Surv. 30, 51–105 (1975)

Veselov, A.: Growth and integrability in the dynamics of mappings. Commun. Math. Phys. 145, 181–193 (1992)