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 Regul. Chaotic Dyn., 2017, Volume 22, Issue 5, Pages 479–501 (Mi rcd271)

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

DOI: https://doi.org/10.1134/S1560354717050021

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Bibliographic databases:

MSC: 37J45, 34C37, 34E20, 34D09
Accepted:26.06.2017
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Citation: Alexey V. Ivanov, “Connecting Orbits near the Adiabatic Limit of Lagrangian Systems with Turning Points”, Regul. Chaotic Dyn., 22:5 (2017), 479–501

Citation in format AMSBIB
\Bibitem{Iva17} \by Alexey V. Ivanov \paper Connecting Orbits near the Adiabatic Limit of Lagrangian Systems with Turning Points \jour Regul. Chaotic Dyn. \yr 2017 \vol 22 \issue 5 \pages 479--501 \mathnet{http://mi.mathnet.ru/rcd271} \crossref{https://doi.org/10.1134/S1560354717050021} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412030900002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030157552} 

• http://mi.mathnet.ru/eng/rcd271
• http://mi.mathnet.ru/eng/rcd/v22/i5/p479

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V A. Ivanov, “Transversal connecting orbits of Lagrangian systems with turning points: Newton-Kantorovich method”, 2018 Days on Diffraction (DD), eds. O. Motygin, A. Kiselev, L. Goray, A. Kazakov, A. Kirpichnikova, M. Perel, IEEE, 2018, 149–154