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.
([c] Ringgold, Inc., Portland, OR)
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|Article Type:||Brief article|
|Date:||Apr 1, 2014|
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