Whiskered tori with prefixed frequencies and Lyapunov spectrum

References

• Arnol'd V.I. Proof of ANKolmogorov's theorem on the preservation of quasi-periodic motions under small perturbations of the Hamiltonian Usp. Mat. Nauk 1963 18 13 40 English translation:Russian Mathematics Surveys 18, 9-36 (1963)
   Google Scholar
• Arnol'd , VI . 1966 . Instability of dynamical systems with several degrees of freedom . Soviet Mathxokl , 5 : 581 – 585 .
   Google Scholar
• Benettin , G and Gallavotti , G . 1986 . Stability of motions near resonances in quasi-integrable . Journal of Statistical Physics , 44 : 293 – 338 .
   Web of Science ®Google Scholar
• Benfatto , G and Gallavotti , G . 1990 . Perturbation theory of the Fermi surface in a quantum liquidA general quasi particle formalism and one dimensional systems . Journal of Statistical Physics , 59 : 541 – 664 .
   Web of Science ®Google Scholar
• Bryuno A.D. The analytic form of differential equations I Transactions of the Moscow actions of the Moscow Mathematical Society 1971 25 131 288 (1971/1972) The analytic form of differential equationsITransactions of the Moscow actions of the Moscow Mathematical Society 26, 195-239, (1972)
   Google Scholar
• Chirikov , BV . 1979 . A universal instability of many dimensional oscillator systems . Physics Reports , 52 : 263 – 379 .
   Web of Science ®Google Scholar
• Chierchia , L and Falcolini , C . 1995 . A direct proof of the theorem by Kolmogorov in Hamiltonian . Annalidella ScuolaNormale Superiore diPisa , 21 : 541 – 593 .
   Google Scholar
• Chierchia , L and Gallavotti , G . 1994 . Drift and diffusion in phase space . AnnInstHPoincare , 60 : 1 – 144 .
   Google Scholar
• Eliasson L.H. Absolutely convergent series expansions for quasi-periodic motions Report 2-88 Department of Mathematics University of Stockholm 1988
   Google Scholar
• Gallavotti , G . 1985 . Renormalization theory and ultraviolet stability for scalar fields via renormaliza- . Review of Modern Physics , 57 : 471 – 572 .
   Web of Science ®Google Scholar
• Gallavotti , G. Invariant tori:a field theoretic point of view on Eliasson's work . Talk at the meeting in honor of the 60th birthday of G. Dell'Antonio . May 1993 , Capri . Marseille, CNRS-CPTpreprint
   Google Scholar
• Gallavotti , G . 1994 . Twistless KAM toriquasi flat homoclinic intersectionsand other cancellations . Review of MathematicalPhysics , 6 : 343 – 411 .
   Google Scholar
• Gallavotti , G . 1994 . Twistless KAM tori . Communications in Mathematical Physics , 164 : 145 – 156 .
   Web of Science ®Google Scholar
• Gallavotti , G and Gentile , G . “ Majorant series convergence for twistless KAM toriPreprint; to ” . In Ergodic Theory and Dynamical Systems
   Google Scholar
• Gentile , G . “ A proof of existence of whiskered tori with quasi flat homoclinic intersections in a ” . In Forum Mathematicum
   Google Scholar
• Graff , SM . 1974 . On the conservation for hyperbolic invariant tori for Hamiltonian systems . Journalof Differential Equations , 15 : 1 – 69 .
   Web of Science ®Google Scholar
• Harary , F and Palmer , E . Graphical Enumeration
   Google Scholar
• Holmes , PJ , Marsden , JE and Izrailev , FM . 1980 . Nearly linear mappings and their applications . Physica ID , 23 : 243 – 266 .
   Google Scholar
• Kolmogorov , AN . 1954 . On conservation of conditionally periodic motions under small perturba- tions of the Hamiltonian . DoklAkadNaukSSSR , 98 : 527 – 530 .
   Google Scholar
• Mel'mkov , VK . 1963 . On the stability of the center for periodic perturbations . Transactions of theMoscow Mathematical Society , 12 : 1 – 57 .
   Google Scholar
• Moser , J and Moser , J . 1967 . Convergent series expansions for quasi-periodic motions . MathAnn , 169 : 136 – 176 .
   Google Scholar