We study connecting orbits of a natural Lagrangian system defined on a complete Riemannian manifold being subjected to action of a non-stationary force field with potential $U(q,t) = f(t)V(q)$. It is assumed that the factor $f(t)$ tends to $\infty$ as $t\to \pm\infty$ and vanishes at unique point $t_{0}\in \mathbb{R}$. Let $X_{+}$, $X_{-}$ denote the sets of isolated critical points of $V(x)$ at which $U(x,t)$ as a function of $x$ distinguishes its maximum for any fixed $t> t_{0}$ and $t
Original languageEnglish
Pages (from-to)510-521
JournalRegular and Chaotic Dynamics
Volume21
Issue number5
DOIs
StatePublished - 2016

    Research areas

  • connecting orbits, homoclinic and heteroclinic orbits, nonautonomous Lagrangian system, variational method

ID: 7592393