09-132 Xia LI & Chong-qing CHENG

Connecting Orbits of Autonomous Lagrangian Systems (592K, Postscript) Aug 3, 09

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Abstract. Different from time-dependednt case, the time-t-section of Mane set of autonomous Lagrangian system is independent of time, thus, it is nowhere disconnected. It induces some difference in the study of dynamics, for instance, Mather's c-equivalence can not exist among those cohomology class if they are not in a flat of the alpha function. In this paoer, we show how to construct connecting orbits in autonomous systems, and propose a modified c-equivalence. We also apply the result to construct diffusionn orbits in an energy surface.

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