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This article is cited in 10 scientific papers (total in 10 papers)
Connecting Orbits near the Adiabatic Limit of Lagrangian Systems with Turning Points
Alexey V. Ivanov Saint-Petersburg State University, Universitetskaya nab. 7/9, Saint-Petersburg, 199034 Russia
Abstract:
We consider a natural Lagrangian system defined on a complete Riemannian
manifold being subjected to action of a time-periodic force field with potential $U(q,t, \varepsilon) = f(\varepsilon t)V(q)$ depending slowly on time.
It is assumed that the factor $f(\tau)$ is periodic and vanishes at least at one point on the period.
Let $X_{c}$ denote a set of isolated critical points of $V(x)$ at which $V(x)$ distinguishes its maximum or minimum.
In the adiabatic limit $\varepsilon \to 0$ we prove the existence of a set $\mathcal{E}_{h}$ such that the system possesses a rich class of doubly
asymptotic trajectories connecting points of $X_{c}$ for $\varepsilon \in \mathcal{E}_{h}$.
Keywords:
connecting orbits, homoclinic and heteroclinic orbits, nonautonomous Lagrangian system, singular perturbation, exponential dichotomy.
Received: 29.05.2017 Accepted: 26.06.2017
Citation:
Alexey V. Ivanov, “Connecting Orbits near the Adiabatic Limit of Lagrangian Systems with Turning Points”, Regul. Chaotic Dyn., 22:5 (2017), 479–501
Linking options:
https://www.mathnet.ru/eng/rcd271 https://www.mathnet.ru/eng/rcd/v22/i5/p479
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Abstract page: | 158 | References: | 35 |
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