On the equations of the hydrodynamic type

Journal of Applied Mathematics and Mechanics - Tập 80 - Trang 209-214 - 2016
V.V. Kozlov1
1V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Tài liệu tham khảo

Gledzer, 1981 Borisov, 2003 Kozlov, 2013 Kozlov, 1988, Invariant measures of Euler–Poincaré equations in Lie algebras, Funkts Anal Prilozh, 22, 69 Volterra, 1897, Sopra una classe di equazioni dinamiche, Att della R Acc delle Scienze di Torino, 32, 452 Bizyaev, 2015, Homogeneous systems with quadratic integrals, Lie–Poisson quasi-brackets, and Kowalewsky's method, Matem Sb, 206, 29 Karapetyan AV, Rumyantsev VV. The stability of conservative and dissipative systems. General Mechanics. Vol. 6. Advances in Science and Technology. Moscow: VINITI; 1983. Arnold, 1998 Kozlov, 1992, Linear systems with a quadratic integral, J Appl Math Mech, 56, 803, 10.1016/0021-8928(92)90114-N Rubanovskii, 1974, On bifurcation and stability of stationary motions in certain problems of dynamics of a solid body, J Appl Math Mech, 38, 573, 10.1016/0021-8928(74)90005-7 Gledzer, 1973, A system of the hydrodynamic type, allowing two quadratic integrals of motion, Dokl Akad Nauk SSSR, 209, 1046 Kozlov, 2007, Dynamical systems with multivalued integrals on a torus, Proc. Steklov Inst Math, 256, 188, 10.1134/S0081543807010105 Williamson, 1936, On the algebraic problem concerning the normal forms of linear dynamical system, Am J Math, 58, 141, 10.2307/2371062 Vershik, 2007, Does there exist a Lebesgue measure in the infinite-dimensional space?, Proc Steklov Inst Math, 259, 10.1134/S0081543807040153 Bogachev, 1997 Frisch, 1995 Poincaré, 1899 Kozlov, 2015, Invariant and quasi-invariant measures on infinite-dimensional spaces, Dokl Math, 92, 743, 10.1134/S1064562415060290 Bizyaev, 2015, Topology and bifurcation in nonholonomic mechanics, Int J Bifur Chaos, 25, 1530028, 10.1142/S0218127415300281 Tatarinov, 1988, Separable and new topological effects in holonomic and non-holonomic systems, Tr Sem Vekt Tenz Anal, XXIII, 160 Yudovich, 1963, Nonstationary flows of an ideal incompressible fluid, Zh Vychisl Matem Matem Fiz, 3, 1032