A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the Large Gap Problem
Author: Amadeu Delshams
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 141
ISBN-13: 9781470404451
DOWNLOAD EBOOK →Beginning by introducing a geometric mechanism for diffusion in a prioriunstable nearly integrable dynamical systems, this book is based onthe observation that resonances, besides destroying the primary KAMtori, create secondary tori and tori of lower dimension. It argues thatthese objects created by resonances can be incorporated in transitionchains taking the place of the destroyed primary KAM tori.The authorsestablish rigorously the existence of this mechanism in a simple modelthat has been studied before. The main technique is to develop a toolkitto study, in a unified way, tori of different topologies and their invariantmanifolds, their intersections as well as shadowing properties of thesebi-asymptotic orbits. This toolkit is based on extending and unifyingstandard techniques.