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Singularity theory for non-twist KAM tori / A. Gonzalez-Enriquez, A. Haro and R. de la Llave.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 227, no 1067.Publication details: Providence : American Mathematical Society, c2014.Description: vi, 115 p. : illustrations ; 26 cmISBN:
  • 9780821890189 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Preliminaries -- 3. Geometric properaties of an invariant torus -- 4. Geometric properties of fibered Lagrangian deformations -- 5. Nondegeneracy on a KAM procedure with fixed frequency -- 6. A KAM theorem for symplectic deformations -- 7. A transformed tori theorem-- 8. Bifurcation theory for KAM tori -- 9. The close-to integrable case. Appendices: Hamiltonian vector fields & Elements of singularity theory-- Bibliography.
Summary: In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 135888
Total holds: 0

"January 2014, volume 227, number 1067 (third of 4 numbers)"--Title page.

Includes bibliographical references (pages 111-115).

1. Introduction --
2. Preliminaries --
3. Geometric properaties of an invariant torus --
4. Geometric properties of fibered Lagrangian deformations --
5. Nondegeneracy on a KAM procedure with fixed frequency --
6. A KAM theorem for symplectic deformations --
7. A transformed tori theorem--
8. Bifurcation theory for KAM tori --
9. The close-to integrable case.
Appendices: Hamiltonian vector fields & Elements of singularity theory--
Bibliography.

In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.

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