Literatur

AbSt72

M. Abramowitz und I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York (1972).

Ar83

V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, New York (1983).

Ar89

V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York (1989).

ArPl90

D. K. Arrowsmith und C. M. Place, An Introduction to Dynamical Systems, Cambridge University Press, Cambridge (1990).

Ba61

V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform I, Comm. Pure Appl. Math. 14 (1961) 187-214.

Bi66

G. D. Birkhoff, Dynamical Systems, AMS, New York (1966).

BrSe85

I. N. Bronstein und K. A. Semendjajew, Taschenbuch der Mathematik, Harri Deutsch, Thun und Frankfurt/Main (1985).

BrGa86

L. S. Brown und G. Gabrielse, Geonium theory: physics of a single electron or ion in a Penning trap, Rev. Mod. Phys. 58 (1986) 233-311.

Ca81

J. R. Cary, Lie transform perturbation theory for Hamiltonian systems, Phys. Rep. 79 (1981) 129-159.

Ch79

B. V. Chirikov, A universal instability of many-dimensional oscillator systems, Phys. Rep. 52 (1979) 263-379.

ChEA83

R. C. Churchill, M. Kummer, D. L. Rod, On averaging, reduction, and symmetry in Hamiltonian systems , J. Diff. Eq. 49 (1983) 359-414.

ChLe84

R. C. Churchill und D. Lee, Harmonic oscillators at low energies, in: D. V. Chudnovsky und G. V. Chudnovsky (Hrsg.), Classical and Quantum Models and Arithmetic Problems, Marcel Dekker Inc., New York (1984) 239-286.

CoVl75

G. Contopoulos und L. Vlahos, Integrals of motion and resonances in a dipole magnetic field, J. Math. Phys. 16 (1975) 1469-1474.

Cr90

P. Crehan, The proper quantum analogue of the Birkhoff-Gustavson method of normal forms, J. Phys. A: Math. Gen. 23 5815-5828.

De69

A. Deprit, Canonical transformations depending on a small parameter, Cel. Mech. 1 (1969) 11-30.

Dr65

A. J. Dragt, Trapped orbits in a magnetic dipole field, Rev. Geophys. 3 (1965) 255-298.

DrFi76a

A. J. Dragt und J. M. Finn, Lie series and invariant functions for analytic symplectic maps, J. Math. Phys. 17 (1976) 2215-2227.

DrFi76b

A. J. Dragt und J. M. Finn, Insolubility of trapped particle motion in a magnetic dipole field, J. Geophys. Res. 81 (1976) 2327-2340.

DrFi79

A. J. Dragt und J. M. Finn, Normal form for mirror machine Hamiltonians, J. Math. Phys. 20 (1979) 2649-2660.

Ec86

B. Eckhardt, Birkhoff-Gustavson normal form in classical and quantum mechanics, J. Phys. A: Math. Gen. 19 (1986) 2961-2972.

ElEA87

C. Elphick, E. Tirapegui, M. E. Brachet, P. Coullet und G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica 29D (1987) 95-127.

EnRe87

G. Engeln-Müllges und F. Reutter, Formelsammlung zur numerischen Mathematik mit C-Programmen, Bibliographisches Institut, Zürich (1987).

Fi86

G. Fischer, Lineare Algebra, Vieweg, Braunschweig (1986).

Ga93

G. Gabrielse, Kühlung und Speicherung von Antiprotonen, Spektrum der Wissenschaft (1993) Nr. 2, 44-51.

Ga68

L. M. Garrido, General interaction picture from action principle for mechanics, J. Math. Phys. 10 (1968) 1045-1056.

Go80

H. Goldstein, Classical Mechanics, Addison-Wesley, Reading (1980).

GuHo83

J. Guckenheimer und P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York (1983).

Gu66

F. G. Gustavson, On constructing formal integrals of a Hamiltonian system near an equilibrium point, Astron. J. 71 (1966) 670-686.

He83

M. Hénon, Numerical exploration of Hamiltonian systems, in: G. Iooss, R. H. G. Hellemann und R. Stora (Hrsg.), Comportement Chaotique des Systèmes Déterministes, North-Holland, Amsterdam (1983).

HeHe64

M. Hénon und C. Heiles, The applicability of the third integral of motion: some numerical experiments, Astron. J. 69 (1964) 73-79.

Hi87

J.  Hietarinta, Direct Methods for the search of the second invariant, Phys. Rep. 147 (1987) 87-154.

HiSm74

M. W. Hirsch und S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York (1974).

Hu87

J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, New York (1987).

IoAd92

G. Iooss und M. Adelmeyer, Topics in Bifurcation Theory and Applications, World Scientific, Singapore (1992).

Je92

G. Jerke, Die Erde hat einen dritten Strahlungsgürtel, Phys. Bl. 48 (1992) 188.

KaRo92

M. Kaluza und M. Robnik, Improved accuracy of the Birkhoff-Gustavson normal form and its convergence properties, J. Phys. A: Math. Gen. 25 (1992) 5311-5327.

La90

K. La Mon, Lie series in an extended region of phase space, J. Phys. A: Math. Gen. 23 (1990) 3875-3884.

LiLi92

A. J. Lichtenberg und M. A. Lieberman, Regular and Chaotic Dynamics, Springer, New York ().

MeHa92

K. R. Meyer und G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer (1992).

Mo68

J. K. Moser, Lectures on Hamiltonian Systems, Mem. Amer. Math. Soc. 81 (1968) 1-60.

Mo73

J. K. Moser, Stable and Random Motions in Dynamical Systems, Princeton University Press, Princeton (1973).

NaSc61

J. Naas und H. L. Schmid, Mathematisches Wörterbuch, Band II, Teubner, Berlin (1961).

Ne77

S. E. Newhouse, Quasi-elliptic points in conservative dynamical systems, Amer. J. Math. 99 (1977) 1061-1087.

No90a

W. Nolting, Grundkurs: Theoretische Physik 2. Analytische Mechanik, Zimmermann-Neufang, Ulmen (1990).

No90b

W. Nolting, Grundkurs: Theoretische Physik 3. Elektrodynamik, Zimmermann-Neufang, Ulmen (1990).

No63

T. G. Northrop, The Adiabatic Motion of Charged Particles, Interscience Publishers, New York (1963).

Oz88

A. M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization, Cambridge University Press, Cambridge (1988).

PaMe82

J. Palis und W. de Melo, Geometric Theory of Dynamical Systems, Springer, New York (1982).

PlEA78

D. Plachky, L. Baringhaus und N. Schmitz, Stochastik I, Akademische Verlagsgesellschaft, Wiesbaden (1978).

Po92

H. Poincaré, Les Méthodes Nouvelles de la Méchanique Céleste (drei Bände), Gauthier-Villars, Paris (1892, 1893, 1899).

Ro70

R. C. Robinson, Generic properties of conservative systems, Amer. J. Math. 92 (1970) 562-603.

Ro84

M. Robnik, The algebraic quantization of the Birkhoff-Gustavson normal form, J. Phys. A: Math. Gen. 17 (1984) 109-130.

SaVe85

J. F. Sanders und F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems, Springer, New York (1985).

Sc89

H. G. Schuster, Deterministic Chaos, VCH, Weinheim (1989).

Se90

B. Seegers, Chaotische Streuung im Störmer-Problem, Diplomarbeit, Westfälische Wilhelms-Universität Münster (1990).

ShRe82

R. B. Shirts und W. P. Reinhardt, Approximate constants of motion for classically chaotic vibrational dynamics: vague tori, semiclassical quantization, and classical intramolecular energy flow, J. Chem. Phys. 77 (1982) 5204-5217. Erratum: J. Chem. Phys. 79 (1983) 3173.

SiMo71

C. L. Siegel und J. K. Moser, Lectures on Celestial Mechanics, Springer, Berlin (1971).

St91

B. Stegemerten, Reguläre und irregulär-chaotische Bewegung in der Penning-Falle, Diplomarbeit, Westfälische Wilhelms-Universität Münster (1991).

St89

J. Stoer, Numerische Mathematik, Springer, Berlin (1989).

St55

C. Størmer, The Polar Aurora, Clarendon Press, Oxford (1955).

St87

N. Straumann, Klassische Mechanik, Springer, Berlin (1987).

SwDe79

R. T. Swimm und J. B. Delos, Semiclassical calculations of vibrational energy levels for nonseparable systems using the Birkhoff-Gustavson normal form, J. Chem. Phys. 71 (1979) 1706-1717.

Wi90

S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York (1990).

Wo91

S. Wolfram, Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, Redwood City (1991).

Ze73

E. Zehnder, Homoclinic points near elliptic fixed points, Comm. Pure Appl. Math. 26 (1973) 131-182.

ZiHä93

C. Zimmermann und T. W. Hänsch, Antiwasserstoff, Phys. Bl. 49 (1993) 193-196.