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, ε) = f(εt)V(q) depending slowly on time. It is assumed that the factor f(τ) 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 ε → 0 we prove the existence of a set E h such that the system possesses a rich class of doubly asymptotic trajectories connecting points of X c for ε ∈ E h .
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Ivanov, A.V. Connecting orbits near the adiabatic limit of Lagrangian systems with turning points. Regul. Chaot. Dyn. 22, 479–501 (2017). https://doi.org/10.1134/S1560354717050021
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DOI: https://doi.org/10.1134/S1560354717050021
Keywords
- connecting orbits
- homoclinic and heteroclinic orbits
- nonautonomous Lagrangian system
- singular perturbation
- exponential dichotomy