First and invariant integrals in stability problems

D. Aeyels, R. Sepulchre, Stability for dynamical systems with first integrals: a topological criterion, Systems and Control Letters, Vol. 19, North-Holland, Amsterdam 1992, pp. 461–465. Bathia, 1970 Chow, 1982 Habets, 1973, Stability criteria for systems with first integrals generalizing theorems of Routh and Salvadori, 570 A.V. Karapetyan, The Routh theorem and its extensions, in: B. Sz-Nagy, L. Hatvanti (Eds.), Colloq. Math. Soc. Janos Bolyai, Qualitative Theory of Differential Equations, Vol. 53, North-Holland, Amsterdam, 1990, pp. 271–290. A.V. Karapetyan, V.V. Rumyantsev, Stability of conservative and dissipative systems, in: A.Y. Ishlinskij, N.N. Krasovskij, V.V. Rumiantsev, V.N. Rubanovskij (Eds.), Appl. Mech. Soviet Reviews, Stability Anal. Mech. Vol. 1, Hemisphere, Washington, DC, 1990, pp. 3–144. Marchetti, 1976, Liapunov direct method in approaching bifurcation problems, Ann. Mat. Pura Appl., 108, 211, 10.1007/BF02413955 Marsden, 1976 Negrini, 1979, Attractivity and Hopf bifurcation, Nonlinear Anal. TMA, 3, 87, 10.1016/0362-546X(79)90039-7 Peiffer, 1994, A stability criterion for periodic systems with first integrals, Rend. Sem. Mat. Univ. Padova, 92, 165 Salvadori, 1953, Un'osservazione su un criterio di stabilità del Routh, Rend. Accad. Sci. Fis. Mat. Nat. Napoli, XX, 269 Salvadori, 1999, First integrals and stability problems, Math. Japon., 49, 1