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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
Autore Delshams Amadeu
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2006
Descrizione fisica 1 online resource (158 p.)
Disciplina 510 s
515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Nonholonomic dynamical systems
Mechanics
Differential equations - Qualitative theory
Soggetto genere / forma Electronic books.
ISBN 1-4704-0445-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Heuristic discussion of the mechanism""; ""2.1. Integrable systems, resonances, secondary tori""; ""2.2. Heuristic description of the mechanism""; ""Chapter 3. A simple model""; ""Chapter 4. Statement of rigorous results""; ""Chapter 5. Notation and definitions, resonances""; ""Chapter 6. Geometric features of the unperturbed problem""; ""Chapter 7. Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds""; ""7.1. Explicit calculations of the perturbed invariant manifold""
""8.5.2. Preliminary analysis of resonances of order one or two""""8.5.3. Primary and secondary tori near the first and second order resonances""; ""8.5.4. Proof of Theorem 8.30 and Corollary 8.31""; ""8.5.5. Existence of stable and unstable manifolds of periodic orbits""; ""Chapter 9. The scattering map""; ""9.1. Some generalities about the scattering map""; ""9.2. The scattering map in our model: definition and computation""; ""Chapter 10. Existence of transition chains""; ""10.1. Transition chains""; ""10.2. The scattering map and the transversality of heteroclinic intersections""
""10.2.1. The non-resonant region and resonances of order 3 and higher""""10.2.2. Resonances of first order""; ""10.2.3. Resonances of order 2""; ""10.3. Existence of transition chains to objects of different topological types""; ""Chapter 11. Orbits shadowing the transition chains and proof of theorem 4.1""; ""Chapter 12. Conclusions and remarks""; ""12.1. The role of secondary tori and the speed of diffusion""; ""12.2. Comparison with [DLS00]""; ""12.3. Heuristics on the genericity properties of the hypothesis and the phenomena""; ""12.4. The hypothesis of polynomial perturbations""
""12.5. Involving other objects""""12.6. Variational methods""; ""12.7. Diffusion times""; ""Chapter 13. An example""; ""Acknowledgments""; ""Bibliography""
Record Nr. UNINA-9910480091103321
Delshams Amadeu  
Providence, Rhode Island : , : American Mathematical Society, , 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
Autore Delshams Amadeu
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2006
Descrizione fisica 1 online resource (158 p.)
Disciplina 510 s
515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Nonholonomic dynamical systems
Mechanics
Differential equations - Qualitative theory
ISBN 1-4704-0445-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Heuristic discussion of the mechanism""; ""2.1. Integrable systems, resonances, secondary tori""; ""2.2. Heuristic description of the mechanism""; ""Chapter 3. A simple model""; ""Chapter 4. Statement of rigorous results""; ""Chapter 5. Notation and definitions, resonances""; ""Chapter 6. Geometric features of the unperturbed problem""; ""Chapter 7. Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds""; ""7.1. Explicit calculations of the perturbed invariant manifold""
""8.5.2. Preliminary analysis of resonances of order one or two""""8.5.3. Primary and secondary tori near the first and second order resonances""; ""8.5.4. Proof of Theorem 8.30 and Corollary 8.31""; ""8.5.5. Existence of stable and unstable manifolds of periodic orbits""; ""Chapter 9. The scattering map""; ""9.1. Some generalities about the scattering map""; ""9.2. The scattering map in our model: definition and computation""; ""Chapter 10. Existence of transition chains""; ""10.1. Transition chains""; ""10.2. The scattering map and the transversality of heteroclinic intersections""
""10.2.1. The non-resonant region and resonances of order 3 and higher""""10.2.2. Resonances of first order""; ""10.2.3. Resonances of order 2""; ""10.3. Existence of transition chains to objects of different topological types""; ""Chapter 11. Orbits shadowing the transition chains and proof of theorem 4.1""; ""Chapter 12. Conclusions and remarks""; ""12.1. The role of secondary tori and the speed of diffusion""; ""12.2. Comparison with [DLS00]""; ""12.3. Heuristics on the genericity properties of the hypothesis and the phenomena""; ""12.4. The hypothesis of polynomial perturbations""
""12.5. Involving other objects""""12.6. Variational methods""; ""12.7. Diffusion times""; ""Chapter 13. An example""; ""Acknowledgments""; ""Bibliography""
Record Nr. UNINA-9910788741103321
Delshams Amadeu  
Providence, Rhode Island : , : American Mathematical Society, , 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara
Autore Delshams Amadeu
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2006
Descrizione fisica 1 online resource (158 p.)
Disciplina 510 s
515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Nonholonomic dynamical systems
Mechanics
Differential equations - Qualitative theory
ISBN 1-4704-0445-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Heuristic discussion of the mechanism""; ""2.1. Integrable systems, resonances, secondary tori""; ""2.2. Heuristic description of the mechanism""; ""Chapter 3. A simple model""; ""Chapter 4. Statement of rigorous results""; ""Chapter 5. Notation and definitions, resonances""; ""Chapter 6. Geometric features of the unperturbed problem""; ""Chapter 7. Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds""; ""7.1. Explicit calculations of the perturbed invariant manifold""
""8.5.2. Preliminary analysis of resonances of order one or two""""8.5.3. Primary and secondary tori near the first and second order resonances""; ""8.5.4. Proof of Theorem 8.30 and Corollary 8.31""; ""8.5.5. Existence of stable and unstable manifolds of periodic orbits""; ""Chapter 9. The scattering map""; ""9.1. Some generalities about the scattering map""; ""9.2. The scattering map in our model: definition and computation""; ""Chapter 10. Existence of transition chains""; ""10.1. Transition chains""; ""10.2. The scattering map and the transversality of heteroclinic intersections""
""10.2.1. The non-resonant region and resonances of order 3 and higher""""10.2.2. Resonances of first order""; ""10.2.3. Resonances of order 2""; ""10.3. Existence of transition chains to objects of different topological types""; ""Chapter 11. Orbits shadowing the transition chains and proof of theorem 4.1""; ""Chapter 12. Conclusions and remarks""; ""12.1. The role of secondary tori and the speed of diffusion""; ""12.2. Comparison with [DLS00]""; ""12.3. Heuristics on the genericity properties of the hypothesis and the phenomena""; ""12.4. The hypothesis of polynomial perturbations""
""12.5. Involving other objects""""12.6. Variational methods""; ""12.7. Diffusion times""; ""Chapter 13. An example""; ""Acknowledgments""; ""Bibliography""
Record Nr. UNINA-9910827755503321
Delshams Amadeu  
Providence, Rhode Island : , : American Mathematical Society, , 2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Autore González-Enríquez A (Alejandra), <1967->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (128 p.)
Disciplina 515.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Bifurcation theory
Perturbation (Mathematics)
Ergodic theory
Soggetto genere / forma Electronic books.
ISBN 1-4704-1428-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910480615103321
González-Enríquez A (Alejandra), <1967->  
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Autore González-Enríquez A (Alejandra), <1967->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (128 p.)
Disciplina 515.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Bifurcation theory
Perturbation (Mathematics)
Ergodic theory
ISBN 1-4704-1428-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910796031603321
González-Enríquez A (Alejandra), <1967->  
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
Autore González-Enríquez A (Alejandra), <1967->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (128 p.)
Disciplina 515.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Bifurcation theory
Perturbation (Mathematics)
Ergodic theory
ISBN 1-4704-1428-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910828119103321
González-Enríquez A (Alejandra), <1967->  
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui