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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom(AMS-208)$
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Vadim Kaloshin and Ke Zhang

Print publication date: 2020

Print ISBN-13: 9780691202525

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691202525.001.0001

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Variational Aspects Of The Slow Mechanical System

Variational Aspects Of The Slow Mechanical System

Chapter:
(p.182) Chapter Fifteen Variational Aspects Of The Slow Mechanical System
Source:
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
Author(s):

Kaloshin Vadim

Zhang Ke

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691202525.003.0015

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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