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This article is cited in 3 scientific papers (total in 3 papers)
Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field
Alexey V. Ivanov Saint-Petersburg State University,
Universitetskaya nab. 7/9, Saint-Petersburg, 199034 Russia
Abstract:
We study connecting orbits of a natural Lagrangian system defined on a complete Riemannian manifold subjected to the action of a nonstationary 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 a 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 $t < t_{0}$, respectively. Under nondegeneracy conditions on points of $X_\pm$ we prove the existence of infinitely many doubly asymptotic trajectories connecting $X_{-}$ and $X_{+}$.
Keywords:
connecting orbits, homoclinic and heteroclinic orbits, nonautonomous Lagrangian system, variational method.
Received: 10.05.2016 Accepted: 09.08.2016
Citation:
Alexey V. Ivanov, “Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field”, Regul. Chaotic Dyn., 21:5 (2016), 510–521
Linking options:
https://www.mathnet.ru/eng/rcd200 https://www.mathnet.ru/eng/rcd/v21/i5/p510
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Abstract page: | 162 | References: | 27 |
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