TY - JOUR

T1 - Connecting orbits of Lagrangian systems in non-stationary force field

AU - Ivanov, A. V.

PY - 2016

Y1 - 2016

N2 - 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

AB - 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

KW - connecting orbits

KW - homoclinic and heteroclinic orbits

KW - nonautonomous Lagrangian system

KW - variational method

U2 - 10.1134/S1560354716050026

DO - 10.1134/S1560354716050026

M3 - Article

VL - 21

SP - 510

EP - 521

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 5

ER -