Perturbation theory and control in classical or quantum mechanics by an inversion formula

Journal of Physics A: Mathematical and General

Volumn 37, Issue 24, 2004, Pages 6337-6357

  Vittot, Michel ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042563335     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/24/011     Document Type: Article

References (14)

1. Bellissard J and Vittot M 1990 Heisenberg's picture and non commutative geometry of the semi classical limit in quantum mechanics Ann. Inst. Henri Poincaré A 52 175-235
2. Carletti T 2003 The Lagrange inversion formula on non-Archimedean fields non-analytical form of differential and finite difference equations Discrete Continuous Dyn. Syst. A 9 835-58 (Preprint math/0110135)
3. Ciraolo G, Chandre C, Lima R, Vittot M and Pettini M 2004 Control of chaos in Hamiltonian systems Celest. Mech. Dyn. Astron. at press (Preprint nlin.CD/0311009)
4. Ciraolo G, Chandre C, Lima R, Pettini M, Vittot M, Figarella Ch and Ghendrih Ph 2004 Controlling chaotic transport in an Hamiltonian model of interest to magnetized plasmas J. Phys. A: Math. Gen. 37 3589 (Preprint nlin.CD/0304040)
5. Ciraolo G, Briolle F, Chandre C, Floriani E, Lima R, Vittot M, Pettini M, Figarella C and Ghendrih P 2004 Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas Phys. Rev. E 69 056213
6. Duclos P, Lev O, Stovicek P and Vittot M 2003 Progressive diagonalization and applications Proc. Conf. on Operator Algebras & Mathematical Physics (Constanja 2001) ed R Purice (Bucarest: Theta Foundation) (Preprint math-ph/0405014)
7. Duclos P, Lev O, Stovicek P and Vittot M 2002 Weakly regular Floquet Hamiltonians with pure point spectrum Rev. Math. Phys. 14 1-38 (Preprint math-ph/0103041)
8. Eliasson L H 1989 Hamiltonian systems with linear normal form near an invariant torus Non-Linear Dynamics (Bologne, 1988) ed G Turchetti (Singapore: World Scientific) p 11-29
9. Hamilton R S 1982 The inverse function theorem of Nash and Moser Bull. Am. Math. Soc. (N.S.) 7 65-222
10. Joye A and Pfister Ch-Ed 1999 Exponential estimates in adiabatic quantum evolution Int. Congress of Mathematical Physics (ICMP 1997) vol 6 ed C De Wit Bracken, J Gould and W Pearce (Cambridge: International Press) pp 309-15
11. Moser J 1961 A new technique for the construction of solutions of nonlinear differential equations Proc. Natl. Acad. Sci. USA 47 1824-31
12. Nash J 1956 The imbedding problem for Riemannian manifolds Ann. Math. 63 20-63
13. Pettini M 1989 Low dimensional Hamiltonian models for non-collisional diffusion of charged particles Non-Linear Dynamics (Bologne, 1988) ed G Turchetti (Singapore: World Scientific) p 287-96
14. Vittot M 1991 Lindstedt perturbation series in Hamiltonian mechanics: explicit formulation via a multidimensional Bümiann-Lagrange formula Preprint CNRS Luminy CPT-91/P.2603(Marseille) http://ccdb3fs.kek.jp/cgi-bin/img/ allpdf? 199204265