04235nam 2200625 450 991079603160332120170822144418.01-4704-1428-7(CKB)3780000000000304(EBL)3114141(SSID)ssj0001034814(PQKBManifestationID)11620926(PQKBTitleCode)TC0001034814(PQKBWorkID)11028909(PQKB)10008860(MiAaPQ)EBC3114141(RPAM)17875929(PPN)195408527(EXLCZ)99378000000000030420150417h20132013 uy 0engur|n|---|||||txtccrSingularity theory for non-twist KAM tori /A. González-Enríquez, A. Haro, R. de la LlaveProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (128 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 227, Number 1067"Volume 227, Number 1067 (third of 4 numbers)."0-8218-9018-2 Includes bibliographical references.""Contents""; ""Part 1 . Introduction and preliminaries""; ""Chapter 1. Introduction""; ""1.1. Towards a singularity theory for KAM tori""; ""1.2. Methodology (a brief description)""; ""1.3. Outline of this monograph""; ""Chapter 2. Preliminaries""; ""2.1. Elementary notations""; ""2.2. Geometric preliminaries""; ""2.3. Symplectic deformations and moment maps""; ""2.4. Analytic preliminaries""; ""2.5. Cohomology equations""; ""Part 2 . Geometrical properties of KAM invariant tori""; ""Chapter 3. Geometric properties of an invariant torus""; ""3.1. Automatic reducibility""""3.2. Geometric definition of non-twist tori""""3.3. Intrinsic character of the reducibility and of the torsion""; ""Chapter 4. Geometric properties of fibered Lagrangian deformations""; ""4.1. The potential of a fibered Lagrangian deformation""; ""4.2. A parametric version of the potential""; ""Part 3 . KAM results""; ""Chapter 5. Nondegeneracy on a KAM procedure with fixed frequency""; ""5.1. Approximate reducibility of approximately invariant tori""; ""5.2. Dummy and modifying parameters""; ""Chapter 6. A KAM theorem for symplectic deformations""""6.1. Functional equations and nondegeneracy condition""""6.2. Statement of the KAM theorem""; ""6.3. Proof of the KAM Theorem""; ""Chapter 7. A Transformed Tori Theorem""; ""7.1. Nondegeneracy condition""; ""7.2. Statement of the Transformed Tori Theorem""; ""7.3. Proof of the Transformed Tori Theorem""; ""Part 4 . Singularity theory for KAM tori""; ""Chapter 8. Bifurcation theory for KAM tori""; ""8.1. Classification of KAM invariant tori""; ""8.2. Local equivalence of Bifurcations diagrams""; ""Chapter 9. The close-to-integrable case""; ""9.1. The integrable case""""9.2. Persistence of invariant tori in quasi-integrable systems""""9.3. Unfolding non-twist tori""; ""9.4. The Birkhoff potential and the potential of an invariant torus""; ""Appendices""; ""Appendix A. Hamiltonian vector fields""; ""A.1. Cohomology equations""; ""A.2. Automatic reducibility of invariant tori""; ""A.3. Families of Hamiltonians and moment maps""; ""A.4. Potential and moment of an invariant FLD""; ""A.5. Transformed Tori Theorem""; ""A.6. A KAM Theorem for families of Hamiltonians""; ""Appendix B. Elements of singularity theory""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 227, Number 1067.Bifurcation theoryPerturbation (Mathematics)Ergodic theoryBifurcation theory.Perturbation (Mathematics)Ergodic theory.515.39González-Enríquez A(Alejandra),1967-1519489Haro A(Alex),1969-De la Llave Rafael1957-MiAaPQMiAaPQMiAaPQBOOK9910796031603321Singularity theory for non-twist KAM tori3757636UNINA