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101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 12$aA geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem $eheuristics and rigorous verification on a model /$fAmadeu Delshams, Rafael de la Llave, Tere M. Seara
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2006.
215   $a1 online resource (158 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 844
300   $a"January 2006, volume 179, number 844 (third of 5 numbers)."
311   $a0-8218-3824-5 
320   $aIncludes bibliographical references (pages 137-141).
327   $a""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""
327   $a""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""
327   $a""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""
327   $a""12.5. Involving other objects""""12.6. Variational methods""; ""12.7. Diffusion times""; ""Chapter 13. An example""; ""Acknowledgments""; ""Bibliography""
410  0$aMemoirs of the American Mathematical Society ;$vno. 844.
606   $aNonholonomic dynamical systems
606   $aMechanics
606   $aDifferential equations$xQualitative theory
615  0$aNonholonomic dynamical systems.
615  0$aMechanics.
615  0$aDifferential equations$xQualitative theory.
676   $a510 s
676   $a515/.39
700   $aDelshams$b Amadeu$01567034
702   $aDe la Llave$b Rafael$f1957-
702   $aSeara$b Tere M.$f1961-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910788741103321
996   $aA geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem$93838112
997   $aUNINA