The existence of homoclinic motions
A motion of a Hamiltonian system is said to be homoclinic, or doubly- periodic, if it tends asymptotically to a periodic motion as \(t\to\pm \infty\). The main result of the concisely written paper is presented in the form of the following theorem: Let \(\gamma\) be a minimal periodic motion with non-vanishing characteristic determinants. Then a homoclinic motion to \(\gamma\) exists. Morse theory is employed to prove the theorem. To understand the paper the reader should be acquainted with two previous contributions by the author [Vestn. Mosk. Univ., Ser. I 1978, No.6, 72-77 (1978; Zbl 0403.34053)] and by \textit{V. V. Kozlov} and the author [ibid. 1980, No.4, 84-89 (1980; Zbl 0439.70020)].
scientific article; zbMATH DE number 3876256