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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom (ams-208).
The first complete proof of Arnold diffusion--one of the most important problems in dynamical systems and mathematical physicsArnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical phy...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2020.
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| Colección: | Annals of mathematics studies.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | JSTOR_on1202461041 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
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| 008 | 201031s2020 nju o ||| 0 eng d | ||
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| 066 | |c (S | ||
| 020 | |a 9780691204932 |q (electronic bk.) | ||
| 020 | |a 0691204934 |q (electronic bk.) | ||
| 029 | 1 | |a AU@ |b 000068213024 | |
| 035 | |a (OCoLC)1202461041 | ||
| 037 | |a 22573/ctvzj7w8c |b JSTOR | ||
| 050 | 4 | |a QA614.83 |b .K35 2020eb | |
| 082 | 0 | 4 | |a 514.74 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Kaloshin, Vadim. | |
| 245 | 1 | 0 | |a Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom |h [electronic resource] : |b (ams-208). |
| 260 | |a Princeton : |b Princeton University Press, |c 2020. | ||
| 300 | |a 1 online resource (219 p.). | ||
| 490 | 1 | |a Annals of Mathematics Studies ; |v v.391 | |
| 500 | |a Description based upon print version of record. | ||
| 505 | 0 | |a Cover -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgments -- I Introduction and the general scheme -- 1 Introduction -- 1.1 Statement of the result -- 1.2 Scheme of diffusion -- 1.3 Three regimes of diffusion -- 1.4 The outline of the proof -- 1.5 Discussion -- 2 Forcing relation -- 2.1 Sufficient condition for Arnold diffusion -- 2.2 Diffusion mechanisms via forcing equivalence -- 2.3 Invariance under the symplectic coordinate changes -- 2.4 Normal hyperbolicity and Aubry-Mather type -- 3 Normal forms and cohomology classes at single resonances | |
| 505 | 8 | |a 5.4 Jump from non-simple homology to simple homology -- 5.5 Forcing equivalence at the double resonance -- II Forcing relation and Aubry-Mather type -- 6 Weak KAM theory and forcing equivalence -- 6.1 Periodic Tonelli Hamiltonians -- 6.2 Weak KAM solution -- 6.3 Pseudographs, Aubry, Mañé, and Mather sets -- 6.4 The dual setting, forward solutions -- 6.5 Peierls barrier, static classes, elementary solutions -- 6.6 The forcing relation -- 6.7 The Green bundles -- 7 Perturbative weak KAM theory -- 7.1 Semi-continuity -- 7.2 Continuity of the barrier function | |
| 505 | 8 | |a 7.3 Lipschitz estimates for nearly integrable systems -- 7.4 Estimates for nearly autonomous systems -- 8 Cohomology of Aubry-Mather type -- 8.1 Aubry-Mather type and diffusion mechanisms -- 8.2 Weak KAM solutions are unstable manifolds -- 8.3 Regularity of the barrier functions -- 8.4 Bifurcation type -- III Proving forcing equivalence -- 9 Aubry-Mather type at the single resonance -- 9.1 The single maximum case -- 9.2 Aubry-Mather type at single resonance -- 9.3 Bifurcations in the double maxima case -- 9.4 Hyperbolic coordinates -- 9.5 Normally hyperbolic invariant cylinder | |
| 505 | 8 | |a 9.6 Localization of the Aubry and Mañé sets -- 9.7 Genericity of the single-resonance conditions -- 10 Normally hyperbolic cylinders at double resonance -- 10.1 Normal form near the hyperbolic fixed point -- 10.2 Shil'nikov's boundary value problem -- 10.3 Properties of the local maps -- 10.4 Periodic orbits for the local and global maps -- 10.5 Normally hyperbolic invariant manifolds -- 10.6 Cyclic concatenations of simple geodesics -- 11 Aubry-Mather type at the double resonance -- 11.1 High-energy case -- 11.2 Simple non-critical case -- 11.3 Simple critical case | |
| 500 | |a 11.3.1 Proof of Aubry-Mather type using local coordinates. | ||
| 520 | |a The first complete proof of Arnold diffusion--one of the most important problems in dynamical systems and mathematical physicsArnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two-and-a-half degrees of freedom).This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Hamiltonian systems. | |
| 650 | 0 | |a Diffusion |x Mathematical models. | |
| 650 | 6 | |a Systèmes hamiltoniens. | |
| 650 | 6 | |a Diffusion (Physique) |x Modèles mathématiques. | |
| 650 | 7 | |a SCIENCE / Mechanics / Dynamics. |2 bisacsh | |
| 650 | 7 | |a Diffusion |x Mathematical models |2 fast | |
| 650 | 7 | |a Hamiltonian systems |2 fast | |
| 700 | 1 | |a Zhang, Ke. | |
| 776 | 0 | 8 | |i Print version: |a Kaloshin, Vadim |t Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (ams-208) |d Princeton : Princeton University Press,c2020 |z 9780691202532 |
| 830 | 0 | |a Annals of mathematics studies. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvzgb6zj |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 3.1 Resonant component and non-degeneracy conditions -- 3.2 Normal form -- 3.3 The resonant component -- 4 Double resonance: geometric description -- 4.1 The slow system -- 4.2 Non-degeneracy conditions for the slow system -- 4.3 Normally hyperbolic cylinders -- 4.4 Local maps and global maps -- 5 Double resonance: forcing equivalence -- 5.1 Choice of cohomologies for the slow system -- 5.2 Aubry-Mather type at a double resonance -- 5.3 Connecting to ΓK1,K2 and Γ^SR K1 -- 5.3.1 Connecting to the double resonance point -- 5.3.2 Connecting single and double resonance | |
| 938 | |a EBSCOhost |b EBSC |n 2404582 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6367392 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37731136 | ||
| 938 | |a De Gruyter |b DEGR |n 9780691204932 | ||
| 994 | |a 92 |b IZTAP | ||