Variational Aspects Of The Slow Mechanical System
Variational Aspects Of The Slow Mechanical System
This chapter describes the variational property of the slow mechanical system. The main goal is to derive some properties of the “channel” and information about the Aubrey sets. More precisely, the chapter proves Proposition 5.1. It provides a condition for the “width” of the channel to be non-zero. The chapter then discusses the limit of the set, which corresponds to the “bottom” of the channel. It drops all subscripts “s” to simplify the notations. The results proved in the chapter are mostly contained in John Mather's works. The chapter reformulates some of them for its purpose and also provides some different proofs.
Keywords: variational property, slow mechanical system, Aubrey sets, John Mather, channel
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