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Singularity Theory for Non-Twist KAM Tori.


Singularity Theory for Non-Twist KAM Tori

A. Gonzalez-Enriquez, A. Haro, and R. de la Llave

American Mathematical Society



Memoirs of the American Mathematical Society; Volume 227; Number 1067


This mathematics monograph on KAM tori with fixed Diophantine frequency from Gonzalez-Enriquez, Haro, and de la Llave is presented in four parts. The preliminary chapters discuss singularity theory for KAM tori, review methodology and present a flow chart of the monograph, and present notation, geometric and analytic background, symplectic deformations, and cohomology equations. Part 2 discusses geometric properties of KAM invariant tori including the case of fibered Lagrangian deformation. Part 3 presents main results, formulating a nondegeneracy condition on a KAM procedure to guarantee finding tori with fixed frequency, and proving a KAM theorem for symplectic deformations and a transformed tori theorem. Finally, part 4 addresses singularity theory in more detail, discussing bifurcation theory and the close-to-integrable case. Appendices cover Hamiltonian vector fields and elements of singularity theory.

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Publication:Reference & Research Book News
Article Type:Brief article
Date:Apr 1, 2014
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